Answering this question  requires understanding what is meant by "Lorentz transformations" and the "CPT transformation."

Lorentz transformations come in two basic types, rotations and boosts.

• There are three possible basic types of rotation, one about each of the three spatial directions.
• A boost is a change of velocity. There are also three possible basic types of boost, one along each of the three spatial directions.

The CPT transformation is formed by combining three transformations: charge conjugation (C), parity inversion (P), and time reversal (T).

• C converts a particle into its antiparticle.
• P transforms an object into its mirror image but turned upside down.
• T changes the direction of flow of time.

A physical system is said to have "Lorentz symmetry" if the relevant laws of physics are unaffected by Lorentz transformations (rotations and boosts). Similarly, a system is said to have "CPT symmetry" if the physics is unaffected by the combined transformation CPT. These symmetries are the basis for Einstein's relativity.

Experiments show to exceptionally high precision that all the basic laws of nature seem to have both Lorentz and CPT symmetry. Experimental results are compiled in the paper Data Tables for Lorentz and CPT Violation.

Note: CPT is the only combination of C, P, T that is presently observed to be an exact symmetry of nature.

The CPT theorem is a very general theoretical result linking Lorentz and CPT symmetry. Roughly, it states that certain theories (local quantum field theories) with Lorentz symmetry must also have CPT symmetry. These theories include all the ones used to describe known particle physics (for example, electrodynamics or the Standard Model) and many proposed theories (for example, Grand Unified Theories).

The CPT theorem can be used to show that a particle and its antiparticle must have certain identical properties, including mass, lifetime, and size of charge and magnetic moment.

Many texts discuss the CPT theorem and its implications. See, for example, R.G. Sachs, The Physics of Time Reversal (University of Chicago Press, Chicago, 1987). 

The existence of high-precision experimental tests together with the general proof of the CPT theorem for Lorentz-symmetric theories implies that the observation of Lorentz or CPT violation would be a sensitive signal for unconventional physics. This means it's interesting to consider possible theoretical mechanisms through which Lorentz or CPT symmetry might be violated.

It is relatively easy to write down a phenomenological description of Lorentz or CPT violation, without attempting to create a consistent theory for the effects. However, without an underlying theory one cannot know whether the phenomenology could be relevant to nature or how plausible it really is.

In contrast, it is relatively difficult to find a theoretically compelling description of Lorentz or CPT violation because Lorentz and CPT symmetry is deeply ingrained into the structure of modern theories of nature. Most published suggestions for a theory of Lorentz or CPT violation either have physical features that seem unlikely to be realized in nature or involve radical revisions of conventional quantum field theory, or both.

In a series of publications dating from 1989 (see bibliography below), we have developed what appears to be a promising theoretical framework to describe Lorentz and CPT violation that is compatible both with experimental constraints and with established quantum field theory.

The theory suggests that apparent breaking of CPT and Lorentz symmetry might be observable in existing or feasible experiments, and it leads to a general phenomenology for CPT and Lorentz violation at the level of the Standard Model of particle physics and Einstein's theory of gravity, General Relativity. Other standard theories such as Quantum Electrodynamics are recovered as special cases.

All elementary particles and their nongravitational interactions are very successfully described by a theory called the Standard Model of particle physics. At the classical level, gravity is well described by Einstein's General Relativity. Both these theories have local Lorentz symmetry.

We have constructed a generalization of the usual Standard Model and General Relativity that has all the conventional desirable properties but that allows for violations of Lorentz and CPT symmetry. This theory is called the Standard-Model Extension, or SME.

The Standard-Model Extension provides a quantitative description of Lorentz and CPT violation, controlled by a set of coefficients whose values are to be determined or constrained by experiment.

A type of converse to the CPT theorem has recently been proved under mild assumptions: if CPT is violated, then Lorentz symmetry is too. This implies any observable CPT violation is described by the Standard-Model Extension. See O.W. Greenberg, Phys. Rev. Lett. 89, 231602 (2002), archived preprint.

Violations of all the symmetries C, P, T, CP are predicted by the Standard Model of particle physics and are observed in experiments. Only the combination CPT is required by the Standard Model to be a symmetry of nature. For example, processes are known in nature that violate C but not CPT.

The Standard-Model Extension allows for violations of Lorentz and CPT symmetry that cannot occur in the usual Standard Model or Einstein's General Relativity. 

We have shown, for instance, that  it allows for CPT violation unaccompanied by C or P or CP violation, causing effects such as a difference between the spectra of hydrogen and antihydrogen. Similarly, it allows for CPT violation unaccompanied by P or T or PT violation, producing effects such as modifications of the behavior of kaons and antikaons. All these effects are forbidden in conventional theories obeying the CPT theorem.

A particularly interesting and conceivably physical source of Lorentz and CPT violation is spontaneous symmetry breaking. This common physical effect occurs when a symmetry of the dynamics is not respected by the solutions of the theory.

For example, the dynamical forces controlling the interactions between planets in Newtonian gravity have rotational symmetry, but the solution of the theory representing our solar system exhibits a definite orientation in space given by the plane of the solar system. Another example is the spontaneous breaking of the electroweak gauge symmetry in the Standard Model.

We have proposed that, even if the underlying theory of nature has Lorentz and CPT symmetry, the vacuum solution of the theory could spontaneously violate these symmetries. This is an attractive way of breaking Lorentz and CPT symmetry because the dynamics remains symmetric and so desirable features of the symmetry are preserved.

The usual Standard Model doesn't have the dynamics necessary to cause spontaneous Lorentz and CPT violation. However, spontaneous breaking could occur in more complicated theories. These may include ones based on extended objects like strings, some of which are known to have dynamics of the necessary type.

As in the usual Standard Model, spontaneous breaking of Lorentz and CPT symmetry is triggered by interactions destabilizing the empty vacuum. In the usual case, the vacuum fills with quantities that are symmetric under Lorentz and CPT transformations (but that violate other symmetries). Here, the vacuum fills instead with quantities that are oriented in the four-dimensional sense, breaking Lorentz invariance and (under some circumstances) CPT.

In this scenario, CPT breaking always implies Lorentz breaking, but not vice versa. The CPT theorem is bypassed because Lorentz symmetry is broken. The underlying theory would then produce the Standard-Model Extension with Lorentz and CPT violation instead of the usual Standard Model.

A technical question sometimes asked is: what happened to the Nambu-Goldstone bosons? For a discrete symmetry like CPT, Goldstone's theorem doesn't apply. For global Lorentz symmetry, it implies that spontaneous breaking must be accompanied by massless bosons. These modes might be identified with the photon. If gravity is included then Lorentz symmetry becomes local. In gauge theories the Nambu-Goldstone bosons could be absorbed to generate masses for the gauge bosons according to the Higgs mechanism, but we have shown the analogue of this effect doesn't occur for gravity. Instead, in some gravitational theories the massless bosons might again be identified with the photon, while in others (with propagating spin connection) the massless bosons can be absorbed to generate mass terms in analogy with the usual Higgs mechanism.

The quick answer is that the Standard-Model Extension has all the properties of the usual Standard Model and General Relativity except that Lorentz and CPT symmetry can be violated.

In the Standard-Model Extension, even one type of Lorentz symmetry remains valid: the theory transforms normally under rotations or boosts of the observer's inertial frame (observer Lorentz transformations). The apparent Lorentz violations appear only when the particle fields are rotated or boosted (particle Lorentz transformations) relative to the vacuum tensor expectation values.

More technically: the full Standard-Model Extension contains all possible coordinate-invariant operators formed by combining Standard-Model and gravitational fields with couplings having Lorentz indices. For most situations at energies well below the scale of the underlying theory, it suffices to study the subset of the full Standard-Model Extension for which the gauge structure and the power-counting renormalizability of the usual Standard Model are unchanged and for which energy and momentum are conserved. The usual quantization methods then apply.

Here is a table listing some of the usual and unusual properties of the Standard-Model Extension in this limit.

USUAL	UNUSUAL
SU(3) x SU(2) x U(1) gauge structure	.
Power-counting renormalizability	.
Energy and momentum conservation	.
SU(2) x U(1) breaking	.
Quantization	.
Microcausality	.
Spin-statistics	.
Observer Lorentz covariance	Particle Lorentz violation
.	CPT violation

As an analogy, consider a conventional particle moving inside a crystal. This is similar to a particle moving in a vacuum with spontaneous Lorentz violation. In a crystal, the particle's behavior typically appears to break both rotations and boost symmetry. However, instead of leading to fundamental problems, the lack of Lorentz symmetry merely results from the presence of the background crystal fields.

The Standard-Model Extension provides a quantitative theoretical framework within which various experimental tests of CPT and Lorentz symmetry can be studied and compared. Potentially observable signals can be deduced in some cases.

Without an explicit fundamental theory, it's very difficult to make any estimates of the size of possible effects. High-precision tests have found no compelling evidence for the violation of Lorentz or CPT symmetry as yet, so any effects must be minuscule.

A very crude estimate of the suppression of possible effects might be made by comparing presently attainable energy scales to the natural scale of an underlying theory including gravity, which involves 17-23 orders of magnitude. Additional suppressions from dimensionless couplings could also appear. Although most experimental tests of CPT and Lorentz symmetry would lack the necessary sensitivity to such signals, a few special ones can already place useful constraints on some of the unconventional terms in the Standard-Model Extension.

In the context of the Standard-Model Extension, one cannot identify a single best test for Lorentz or CPT symmetry because the theory contains different kinds of coefficients to which only certain experiments may be sensitive. For example, the bounds on CPT violation from the measurement of the fractional mass difference between a kaon and an antikaon and those from comparisons of hydrogen and antihydrogen are sensitive to completely different coefficients in the Standard-Model Extension.

We have performed theoretical studies of several kinds of experiments to date, including:

• observations of neutrino oscillations
• observations of neutral-meson oscillations
• clock-comparison tests on Earth and in space
• studies of the motion of a spin-polarized torsion pendulum
• spectroscopy of hydrogen and antihydrogen
• comparative tests of QED in Penning traps
• determination of muon properties
• measurements of cosmological birefringence
• tests with microwave cavities and lasers
• observation of the baryon asymmetry
• measurements of gravitational waves
• tests of post-Newton gravity

See the bibliography for details of our theoretical analyses. Animations of some of the predicted effects are available.

A compilation of experimental results can be found in the Data Tables for Lorentz and CPT Violation, paper 56 in the bibliography. This work has been updated annually since 2008.

Some published experimental measurements of coefficients for Lorentz and CPT violation in the Standard-Model Extension are described in the following references.

• Neutrino oscillations:
  CUPID Collaboration, O. Azzolini et al., Phys. Rev. D 100, 092002 (2019) archived manuscript
  NEMO-3 Collaboration, R. Arnold et al., Eur. Phys. J. C 79, 440 (2019) archived manuscript
  SNO Collaboration, B. Aharmin et al., Phys. Rev. D 98, 112013 (2018) archived manuscript
  Aurora Collaboration, A.S. Barabash et al., Phys. Rev. D 98, 092007 (2018) archived manuscript
  Daya Bay Collaboration, D. Adey et al., Phys. Rev. D, 98, 092013 (2018) archived manuscript
  IceCube Collaboration, M.G. Aartsen et al., Nature Physics, 14, 961 (2018) archived manuscript
  T2K Collaboration, K. Abe et al., Phys. Rev. D 95, 111101 (2017) archived manuscript
  T2K Collaboration, B. Quilain, in CPT and Lorentz Symmetry VII, op. cit., p.125
  EXO-200 Collaboration, J.B. Albert et al., Phys. Rev. D 93, 072001 (2016) archived manuscript
  Super-Kamiokande Collaboration, K. Abe et al., Phys. Rev. D 91, 052003 (2015) archived manuscript
  Super-Kamiokande Collaboration, T. Akiri, in CPT and Lorentz Symmetry VI, op. cit., p.99 archived manuscript
  J.S. Diaz, T. Katori, J. Spitz, and J. Conrad, Phys. Lett. B 727, 412 (2013) archived manuscript
  T. Katori and J. Spitz, in CPT and Lorentz Symmetry VI, op. cit., p.9 archived manuscript
  B. Rebel and S. Mufson, Astropart. Phys. 48, 78 (2013) archived manuscript
  Double Chooz Collaboration, Y. Abe et al., Phys. Rev. D 86, 112009 (2012) archived manuscript
  MiniBooNE Collaboration, T. Katori, Mod. Phys. Lett. A 27, 1230024 (2012) archived manuscript
  MINOS Collaboration, P. Adamson et al., Phys. Rev. D 85, 031101 (2012) archived manuscript
  MiniBooNE Collaboration, A.A. Aguilar-Arevalo et al., Phys. Lett. B 718, 1303 (2013) archived manuscript
  IceCube Collaboration, R. Abbasi et al., Phys. Rev. D 82, 112003 (2010) archived manuscript
  MiniBooNE Collaboration, T. Katori, in CPT and Lorentz Symmetry V, op. cit., p.70 archived manuscript
  MINOS Collaboration, P. Adamson et al., Phys. Rev. Lett. 105, 151601 (2010) archived manuscript
  MINOS Collaboration, P. Adamson et al., Phys. Rev. Lett. 101, 151601 (2008) archived manuscript
  LSND Collaboration, L.B. Auerbach et al., Phys. Rev. D 72, 076004 (2005) archived manuscript
  
• Kaon oscillations:
  KLOE Collaboration, D. Babusci et al., Phys. Lett. B 730, 89 (2014) archived manuscript
  KLOE Collaboration, A. De Santis, in CPT and Lorentz Symmetry VI, op. cit., p.103
  KLOE Collaboration, A. Di Domenico et al., Found. Phys. 40, 852 (2010) Found. Phys. server
  KLOE Collaboration, A. Di Domenico et al., J. Phys. Conf. Ser. 171, 012008 (2009) J. Phys. server
  KLOE Collaboration, M. Testa et al. archived manuscript
  KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II, op. cit., p.122 archived manuscript
  KTeV Collaboration, Y.B. Hsiung et al., Nucl. Phys. Proc. Suppl. 86, 312 (2000)
  
• Neutral-D oscillations:
  FOCUS Collaboration, J. Link et al., Phys. Lett. B 556, 7 (2003) archived manuscript
  FOCUS Collaboration, R. Gardner, in CPT and Lorentz Symmetry II, op. cit., p.165 archived manuscript
  
• Neutral-B oscillations:
  LHCb Collaboration, R. Aaij et al., Phys. Rev. Lett. 116, 241601 (2016) archived manuscript
  D0 Collaboration, V.M. Abazov et al., Phys. Rev. Lett. 115, 161601 (2015) archived manuscript
  BaBar Collaboration, B. Aubert et al., Phys. Rev. Lett. 100, 131802 (2008) archived manuscript
  BaBar Collaboration, B. Aubert et al., preprint SLAC-PUB-12003 (July 2006) archived manuscript
  BaBar Collaboration, B. Aubert et al., Phys. Rev. D 70, 012007 (2004) archived manuscript
  BaBar Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142002 (2004) archived manuscript
  BaBar Collaboration, B. Aubert et al., preprint SLAC-PUB-9696 archived manuscript
  BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001) archived manuscript
  OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997) archived manuscript
  DELPHI Collaboration, M. Feindt et al., preprint DELPHI 97-98 CONF 80 (1997)
  
• Top quark:
  D0 Collaboration, V.M. Abazov et al., Phys. Rev. Lett. 108, 261603 (2012) archived manuscript
  
• Electroweak sector:
  A. Sytema et al., Phys. Rev. C 94, 025503 (2016) archived manuscript
  S.E. Mueller et al., Phys. Rev. D 88, 071901(R) (2013) archived manuscript
  
• Clock-comparison experiments:
  C. Sanner et al., Nature 567, 204 (2019) archived manuscript
  E. Megidish, J. Broz, N. Greene and H. Haeffner, Phys. Rev. Lett. 122, 123605 (2019) archived manuscript
  T. Pruttivarasin et al., Nature 517, 592 (2015) archived manuscript
  B. Botermann et al., Phys. Rev. Lett. 113, 120405 (2014) archived manuscript
  F. Allmendinger et al., in CPT and Lorentz Symmetry VI, op. cit., p.17 archived manuscript
  M.A. Hohensee et al., Phys. Rev. Lett. 111, 050401 (2013) archived manuscript
  A. Matveev et al., Phys. Rev. Lett. 110, 230801 (2013)
  S.K. Peck et al., Phys. Rev. A 86, 012109 (2012) archived manuscript
  M. Smiciklas et al., Phys. Rev. Lett. 107, 171604 (2011) archived manuscript
  C. Gemmel et al., Phys. Rev. D 82, 111901(R) (2010) archived manuscript
  K. Tullney et al., in CPT and Lorentz Symmetry V, op. cit., p.214 archived manuscript
  J.M. Brown et al., Phys. Rev. Lett. 105, 151604 (2010) archived manuscript
  I. Altarev et al., Phys. Rev. Lett. 103, 081602 (2009) archived manuscript
  T.W. Kornack, G. Vasilakis, and M. Romalis, in CPT and Lorentz Symmetry IV, op. cit., p.206
  P. Wolf et al., Phys. Rev. Lett. 96, 060801 (2006) archived manuscript
  P. Wolf et al. archived manuscript
  P. Wolf et al. archived manuscript
  F. Cane et al., Phys. Rev. Lett. 93, 230801 (2004) archived manuscript
  D.F. Phillips et al., Phys. Rev. D 63, 111101(R) (2001) archived manuscript
  M.A. Humphrey et al., Phys. Rev. A 68, 063807 (2003) archived manuscript
  D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000) archived manuscript
  R. Walsworth et al., AIP Conf. Proc. 539, 119 (2000) archived manuscript
  L.R. Hunter et al., in CPT and Lorentz Symmetry, op. cit., p.180
  
• Muon sector:
  BNL g-2 Collaboration, G.W. Bennett et al., Phys. Rev. Lett. 100, 091602 (2008) archived manuscript
  V.W. Hughes et al., Phys. Rev. Lett. 87, 111804 (2001) archived manuscript
  BNL g-2 Collaboration, M. Deile et al. archived manuscript
  
• Tests in Penning traps:
  C. Smorra et al., Nature 575, 310 (2019)
  C. Smorra et al., Nature 550, 371 (2017)
  H. Nagahama et al., Nature Commun. 8, 14084 (2017)
  S. Ulmer et al., Nature 524, 196 (2015)
  H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999) archived manuscript
  R. Mittleman et al., Phys. Rev. Lett. 83, 2116 (1999)
  G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999)
  
• Tests with a spin-polarized torsion pendulum:
  B. Heckel et al., Phys. Rev. D 78, 092006 (2008) archived manuscript
  B. Heckel et al., Phys. Rev. Lett. 97, 021603 (2006) archived manuscript
  L.-S. Hou et al., Phys. Rev. Lett. 90, 201101 (2003) PRL server
  B. Heckel et al. web manuscript
  
• Photon sector:
  A. Friedman et al., Phys. Rev. D 102, 043008 (2020) archived manuscript
  L. Pogosian et al., Phys. Rev. D 100, 023507 (2019) archived manuscript
  A.S. Friedman et al., Phys. Rev. D 99, 035045 (2019) archived manuscript
  F. Kislat, Symmetry 10, 596 (2018) archived manuscript
  F. Kislat and H. Krawczynski, Phys. Rev. D 95, 083013 (2017) archived manuscript
  S.R. Parker et al., Phys. Lett. A 379, 2681 (2015) archived manuscript
  F. Kislat and H. Krawczynski, Phys. Rev. D 92, 045016 (2015) archived manuscript
  M. Nagel et al., Nature Commun. 6, 8174 (2015) archived manuscript
  A. Lo et al. Phys. Rev. X 6, 011018 (2016) archived manuscript
  Y. Michimura et al., Phys. Rev. D 88, 111101(R) (2013) archived manuscript
  V. Vasileiou et al., Phys. Rev. D 87, 122001 (2013) archived manuscript
  Y. Michimura et al., Phys. Rev. Lett. 110, 200401 (2013) archived manuscript
  F. Baynes, M. Tobar, and A. Luiten, Phys. Rev. Lett. 108, 269801 (2012) PRL server
  F. Baynes, A. Luiten, and M. Tobar, Phys. Rev. D 84, 081101 (2011) archived manuscript
  S. Parker et al., Phys. Rev. Lett. 106, 180401 (2011) archived manuscript
  Fermi GBT and LAT Collaborations, V. Vasileiou, in CPT and Lorentz Symmetry V, op. cit., p.138 archived manuscript
  M.A. Hohensee et al., Phys. Rev. D 82, 076001 (2010) archived manuscript
  J.-P. Bocquet et al., Phys. Rev. Lett. 104, 241601 (2010) archived manuscript
  S. Herrmann et al., Phys. Rev. D 80, 105011 (2009) archived manuscript
  M. Tobar et al., Phys. Rev. D 80, 125024 (2009) archived manuscript
  Ch. Eisele, A.Yu. Nevsky, and S. Schiller, Phys. Rev. Lett. 103, 090401 (2009) PRL server
  S. Reinhardt et al., Nature Physics 3, 861 (2007) Nature server
  H. Mueller et al., Phys. Rev. Lett. 99, 050401 (2007) archived manuscript
  M. Hohensee et al., Phys. Rev. D 75, 049902 (2007) archived manuscript
  P.L. Stanwix et al., Phys. Rev. D 74, 081101(R) (2006) archived manuscript
  J.P. Cotter and B.T.H. Varcoe archived manuscript
  P. Antonini et al., Phys. Rev. A 72, 066102 (2005) archived manuscript
  M. Tobar et al., Phys. Rev. A 72, 066101 (2005) archived manuscript
  S. Herrmann et al., Phys. Rev. Lett. 95, 150401 (2005) archived manuscript
  M. Tobar et al., Lect. Notes Phys. 702, 415 (2006) archived manuscript
  P.L. Stanwix et al., Phys. Rev. Lett. 95, 040404 (2005) archived manuscript
  P. Antonini et al., Phys. Rev. A 71, 050101 (2005) archived manuscript
  M. Tobar et al., Phys. Rev. D 71, 025004 (2005) archived manuscript
  P. Wolf et al., Phys. Rev. D 70, 051902 (2004) archived manuscript
  P. Wolf et al., Gen. Rel. Grav. 36, 2352 (2004) archived manuscript
  H. Mueller et al., Phys. Rev. D 68, 116006 (2003) archived manuscript
  H. Mueller et al., Phys. Rev. Lett. 91, 020401 (2003) archived manuscript
  J. Lipa et al., Phys. Rev. Lett. 90, 060403 (2003) archived manuscript
  
• Gravity sector:
  A. Bourgoin et al., archived manuscript
  MICROSCOPE Collaboration, H. Pihan-le Bars et al., Phys. Rev. Lett. 123, 231102 (2019) archived manuscript
  C.-G. Shao et al., Phys. Rev. Lett. 122, 011102 (2019) archived manuscript
  LIGO, VIRGO, Fermi GBM, INTEGRAL Collaborations, B.P. Abbott et al., Ap. J. 848, L13 (2017) archived manuscript
  C.-G. Shao et al., Phys. Rev. D 97, 024019 (2018) archived manuscript
  A. Bourgoin et al., Phys. Rev. Lett. 119, 201102 (2017) archived manuscript
  C.-G. Shao et al., Phys. Rev. Lett. 117, 071102 (2016) archived manuscript
  A. Bourgoin et al., Phys. Rev. Lett. 117, 241301 (2016) archived manuscript
  C. Le Poncin-Lafitte, A. Hees, and S. Lambert, Phys. Rev. D 94, 125030 (2016) archived manuscript
  A. Hees et al., Phys. Rev. D 92, 064049 (2015) archived manuscript
  C.-G. Shao et al., Phys. Rev. D 91, 102007 (2015) archived manuscript
  J. Long and V.A. Kostelecky, Phys. Rev. D 91, 092003 (2015) archived manuscript
  L. Shao, Phys. Rev. D 90, 122009 (2014) archived manuscript
  L. Shao, Phys. Rev. Lett. 112, 111103 (2014) archived manuscript
  M.A. Hohensee, H. Mueller, and R.B. Wiringa, Phys. Rev. Lett. 111, 151102 (2013) archived manuscript
  M.A. Hohensee, S. Chu, A. Peters, and H. Mueller, Phys. Rev. Lett. 106, 151102 (2011) archived manuscript
  D. Bennett, V. Skavysh, and J. Long, in CPT and Lorentz Symmetry V, op. cit., p.258 archived manuscript
  K.-Y. Chung et al., Phys. Rev. D 80, 016002 (2009) archived manuscript
  H. Mueller et al., Phys. Rev. Lett. 100, 031101 (2008) archived manuscript
  J.B.R. Battat, J.F. Chandler, and C.W. Stubbs, Phys. Rev. Lett. 99, 241103 (2007) archived manuscript
  

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CPT and Lorentz Symmetry VIII, Ralf Lehnert, ed. (World Scientific, Singapore, in press).

CPT and Lorentz Symmetry VII, Alan Kostelecky, ed. (World Scientific, Singapore, 2017).

CPT and Lorentz Symmetry VI, Alan Kostelecky, ed. (World Scientific, Singapore, 2014).
e-book at IU library

CPT and Lorentz Symmetry V, Alan Kostelecky, ed. (World Scientific, Singapore, 2011).
e-book at IU library

CPT and Lorentz Symmetry IV, Alan Kostelecky, ed. (World Scientific, Singapore, 2008).
e-book at IU library

CPT and Lorentz Symmetry III, Alan Kostelecky, ed. (World Scientific, Singapore, 2005).
e-book at IU library

CPT and Lorentz Symmetry II, Alan Kostelecky, ed. (World Scientific, Singapore, 2002).
e-book at IU library

CPT and Lorentz Symmetry, Alan Kostelecky, ed. (World Scientific, Singapore, 1999).

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101. Electromagnetic Flavor-Changing Lepton Decays from Lorentz and CPT Violation,
Alan Kostelecky, Emilie Passemar, and Nathan Sherrill,
Phys. Rev. D 106, 076016 (2022).
Archived preprint

100. Lorentz Violation in Dirac and Weyl Semimetals,
Alan Kostelecky, Ralf Lehnert, Navin McGinnis, Marco Schreck, and Babak Seradjeh,
Phys. Rev. Res. 4, 023106 (2022).
Archived preprint

99. Lorentz Symmetry in Ghost-Free Massive Gravity,
Alan Kostelecky and Robertus Potting,
Phys. Rev. D 104, 104046 (2021).
Archived preprint

98. Searches for Beyond-Riemann Gravity,
Alan Kostelecky and Zonghao Li,
Phys. Rev. D 104, 044054 (2021).
Archived preprint

97. Backgrounds in Gravitational Effective Field Theory,
Alan Kostelecky and Zonghao Li,
Phys. Rev. D 103, 024059 (2021).
Archived preprint

96. Lorentz and CPT Violation in Partons,
Alan Kostelecky, Enrico Lunghi, Nathan Sherrill, and Alexandre Vieira,
JHEP 04, 143 (2020).
Archived preprint
Published version (open access)

95. Searching for CPT Violation with Neutral-Meson Oscillations,
Benjamin Edwards and Alan Kostelecky,
Phys. Lett. B 795, 620 (2019).
Archived preprint
Published version (open access)

94. Gauge Field Theories with Lorentz-Violating Operators of Arbitrary Dimension,
Alan Kostelecky and Zonghao Li,
Phys. Rev. D 99, 056016 (2019).
Archived preprint
Published version (open access)

93. Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields,
Benjamin Edwards and Alan Kostelecky,
Phys. Lett. B 786, 319 (2018).
Archived preprint
Published version (open access)

92. Combined Search for a Lorentz-Violating Force in Short-Range Gravity Varying as the Inverse Sixth Power of Distance,
Cheng-Gang Shao et al.,
Phys. Rev. Lett. 122, 011102 (2019).
Archived preprint

91. Lorentz and CPT Tests with Clock-Comparison Experiments,
Alan Kostelecky and Arnaldo Vargas,
Phys. Rev. D 98, 036003 (2018).
Archived preprint
Published version (open access)

90. Lorentz and Diffeomorphism Violations in Linearized Gravity,
Alan Kostelecky and Matthew Mewes,
Phys. Lett. B 779, 136 (2018).
Archived preprint
Published version (open access)

89. Constraining Anisotropic Lorentz Violation via the Spectral-Lag Transition of GRB 160625B,
Jun-Jie Wei, Xue-Feng Wu, Bin-Bin Zhang, Lang Shao, Peter Meszaros, and Alan Kostelecky,
Ap. J. 842, 115 (2017).
Archived preprint

88. Constraints on Nonmetricity from Bounds on Lorentz Violation,
Joshua Foster, Alan Kostelecky, and Rui Xu,
Phys. Rev. D 95, 084033 (2017).
Archived preprint

87. Testing Local Lorentz Invariance with Short-Range Gravity,
Alan Kostelecky and Matthew Mewes,
Phys. Lett. B 766, 137 (2017).
Archived preprint
Published version (open access)

86. Lorentz Violation and Deep Inelastic Scattering,
Alan Kostelecky, Enrico Lunghi, and Alexandre Vieira,
Phys. Lett. B 769, 272 (2017).
Archived preprint
Published version (open access)

85. Lorentz-Violating Spinor Electrodynamics and Penning Traps,
Yunhua Ding and Alan Kostelecky,
Phys. Rev. D 94, 056008 (2016).
Archived preprint

84. Searching for Photon-Sector Lorentz Violation using Gravitational-Wave Detectors,
Alan Kostelecky, Adrian Melissinos, and Matthew Mewes,
Phys. Lett. B 761, 1 (2016).
Archived preprint
Published version (open access)

83. Combined Search for Lorentz Violation in Short-Range Gravity,
Cheng-Gang Shao et al.,
Phys. Rev. Lett. 117, 071102 (2016).
Archived preprint

82. Testing Local Lorentz Invariance with Gravitational Waves,
Alan Kostelecky and Matthew Mewes,
Phys. Lett. B 757, 510 (2016).
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81. Lorentz and CPT Violation in Top-Quark Production and Decay,
Micheal Berger, Alan Kostelecky, and Zhi Liu,
Phys. Rev. D 93, 036005 (2016).
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80. Constraints on Lorentz Violation from Gravitational Cherenkov Radiation,
Alan Kostelecky and Jay Tasson,
Phys. Lett. B 749, 551 (2015).
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79. Lorentz and CPT Tests in Hydrogen, Antihydrogen, and Related Systems,
Alan Kostelecky and Arnaldo Vargas,
Phys. Rev. D 92, 056002 (2015).
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78. Search for Lorentz Violation in Short-Range Gravity,
Josh Long and Alan Kostelecky,
Phys. Rev. D 91, 092003 (2015).
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77. Short-Range Gravity and Lorentz Violation,
Quentin Bailey, Alan Kostelecky, and Rui Xu,
Phys. Rev. D 91, 022006 (2015).
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76. Laboratory Tests of Lorentz and CPT Symmetry with Muons,
Andre Gomes, Alan Kostelecky, and Arnaldo Vargas,
Phys. Rev. D 90, 076009 (2014).
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75. Testing Relativity with High-Energy Astrophysical Neutrinos,
Jorge Diaz, Alan Kostelecky, and Matthew Mewes,
Phys. Rev. D 89, 043005 (2014).
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74. Fermions with Lorentz-Violating Operators of Arbitrary Dimension,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. D 88, 096006 (2013).
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73. Relativity Violations and Beta Decay,
Jorge Diaz, Alan Kostelecky, and Ralf Lehnert,
Phys. Rev. D 88, 071902(R) (2013).
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72. Constraints on Relativity Violations from Gamma-Ray Bursts,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. Lett. 110, 201601 (2013).
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71. Bipartite Riemann-Finsler Geometry and Lorentz Violation,
Alan Kostelecky, Neil Russell, and Rhondale Tso,
Phys. Lett. B 716, 470 (2012).
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70. Search for Violation of Lorentz Invariance in Top-Quark Pair Production and Decay,
D0 Collaboration, V.M. Abazov et al.,
Phys. Rev. Lett. 108, 261603 (2012).
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69. Neutrinos with Lorentz-Violating Operators of Arbitrary Dimension,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. D 85, 096005 (2012).
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68. Lorentz- and CPT-Violating Models for Neutrino Oscillations,
Jorge Diaz and Alan Kostelecky,
Phys. Rev. D 85, 016013 (2012).
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67. Riemann-Finsler Geometry and Lorentz-Violating Kinematics,
Alan Kostelecky,
Phys. Lett. B 701, 137 (2011).
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66. Three-parameter Lorentz-Violating Texture for Neutrino Mixing,
Jorge Diaz and Alan Kostelecky,
Phys. Lett. B 700, 25 (2011).
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65. Classical Kinematics for Lorentz Violation,
Alan Kostelecky and Neil Russell,
Phys. Lett. B 693, 443 (2010).
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64. CPT Violation and B-Meson Oscillations,
Alan Kostelecky and Rick Van Kooten,
Phys. Rev. D 82, 101702(R) (2010).
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63. Matter-Gravity Couplings and Lorentz Violation,
Alan Kostelecky and Jay Tasson,
Phys. Rev. D 83, 016013 (2011).
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62. Lorentz Violation with an Antisymmetric Tensor,
Brett Altschul, Quentin Bailey, and Alan Kostelecky,
Phys. Rev. D 81, 065028 (2010).
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61. Perturbative Lorentz and CPT Violation for Neutrino and Antineutrino Oscillations,
Jorge Diaz, Alan Kostelecky, and Matthew Mewes,
Phys. Rev. D 80, 076007 (2009).
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60. Electrodynamics with Lorentz-Violating Operators of Arbitrary Dimension,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. D 80, 015020 (2009).
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59. Gravity from Spontaneous Lorentz Violation,
Alan Kostelecky and Robertus Potting,
Phys. Rev. D 79, 065018 (2009).
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58. Prospects for Large Relativity Violations in Matter-Gravity Couplings,
Alan Kostelecky and Jay Tasson,
Phys. Rev. Lett. 102, 010402 (2009).
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57. Astrophysical Tests of Lorentz and CPT Violation with Photons,
Alan Kostelecky and Matthew Mewes,
Ap. J. 689, L1 (2008).
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56. Data Tables for Lorentz and CPT Violation,
Alan Kostelecky and Neil Russell,
Rev. Mod. Phys. 83, 11 (2011).
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55. Constraints on Torsion from Bounds on Lorentz Violation,
Alan Kostelecky, Neil Russell, and Jay Tasson,
Phys. Rev. Lett. 100, 111102 (2008).
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54. Spontaneous Lorentz and Diffeomorphism Violation, Massive Modes, and Gravity,
Robert Bluhm, Shu-Hong Fung, and Alan Kostelecky,
Phys. Rev. D 77, 065020 (2008).
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53. Lorentz-Violating Electrodynamics and the Cosmic Microwave Background,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. Lett. 99, 011601 (2007).
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52. Sensitive Polarimetric Search for Relativity Violations in Gamma-Ray Bursts,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. Lett. 97, 140401 (2006).
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51. Global Three-Parameter Model for Neutrino Oscillations using Lorentz Violation,
Teppei Katori, Alan Kostelecky, and Rex Tayloe,
Phys. Rev. D 74, 105009 (2006).
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50. Signals for Lorentz Violation in Post-Newtonian Gravity,
Quentin Bailey and Alan Kostelecky,
Phys. Rev. D 74, 045001 (2006).
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49. Gravity from Local Lorentz Violation,
Alan Kostelecky and Robertus Potting,
Gen. Rel. Grav. 37, 1675 (2005).
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48. Spontaneous Lorentz Violation and Nonpolynomial Interactions,
Brett Altschul and Alan Kostelecky,
Phys. Lett. B 628, 106 (2005).
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47. Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity,
Robert Bluhm and Alan Kostelecky,
Phys. Rev. D 71, 065008 (2005).
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46. Lorentz-Violating Electrostatics and Magnetostatics,
Quentin Bailey and Alan Kostelecky,
Phys. Rev. D 70, 076006 (2004).
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45. Lorentz Violation and Short-Baseline Neutrino Experiments,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. D 70, 076002 (2004).
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44. Gravity, Lorentz Violation, and the Standard Model,
Alan Kostelecky,
Phys. Rev. D 69, 105009 (2004).
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43. Bound on Lorentz- and CPT-Violating Boost Effects for the Neutron,
F. Cane, D. Bear, D. Phillips, M. Rosen, C. Smallwood, R. Stoner, R. Walsworth, and Alan Kostelecky,
Phys. Rev. Lett. 93, 230801 (2004).
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42. Lorentz and CPT Violation in Neutrinos,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. D 69, 016005 (2004).
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41. Lorentz and CPT Violation in the Neutrino Sector,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. D 70, 031902(R) (2004).
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40. Probing Lorentz and CPT Violation with Space-Based Experiments,
Robert Bluhm, Alan Kostelecky, Charles Lane, and Neil Russell,
Phys. Rev. D 68, 125008 (2003).
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39. Vacuum Photon Splitting in Lorentz-Violating Quantum Electrodynamics,
Alan Kostelecky and Austin Pickering,
Phys. Rev. Lett. 91, 031801 (2003).
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38. Spacetime Varying Couplings and Lorentz Violation,
Alan Kostelecky, Ralf Lehnert, and Malcolm Perry,
Phys. Rev. D 68, 123511 (2003).
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37. Signals for Lorentz Violation in Electrodynamics,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. D 66, 056005 (2002).
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36. Supersymmetry and Lorentz Violation,
Micheal Berger and Alan Kostelecky,
Phys. Rev. D 65, 091701(R) (2002).
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35. One-Loop Renormalization of Lorentz-Violating Electrodynamics,
Alan Kostelecky, Charles Lane, and Austin Pickering,
Phys. Rev. D 65, 056006 (2002).
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34. Clock-Comparison Tests of Lorentz and CPT Symmetry in Space,
Robert Bluhm, Alan Kostelecky, Charles Lane, and Neil Russell,
Phys. Rev. Lett. 88, 090801 (2002).
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33. Cosmological Constraints on Lorentz Violation in Electrodynamics,
Alan Kostelecky and Matthew Mewes,
Phys. Rev. Lett. 87, 251304 (2001).
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32. Background Enhancement of CPT Reach at an Asymmetric Phi Factory,
Nathan Isgur, Alan Kostelecky, and Adam Szczepaniak,
Phys. Lett. B 515, 333 (2001).
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31. Noncommutative Field Theory and Lorentz Violation,
Sean Carroll, Jeffrey Harvey, Alan Kostelecky, Charles Lane, and Takemi Okamoto,
Phys. Rev. Lett. 87, 141601 (2001).
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30. Cross Sections and Lorentz Violation,
Don Colladay and Alan Kostelecky,
Phys. Lett. B 511, 209 (2001).
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29. CPT, T, and Lorentz Violation in Neutral-Meson Oscillations,
Alan Kostelecky,
Phys. Rev. D 64, 076001 (2001).
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28. Analogue Models for T and CPT Violation in Neutral-Meson Oscillations,
Alan Kostelecky and Agnes Roberts,
Phys. Rev. D 63, 096002 (2001).
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27. Stability, Causality, and Lorentz and CPT Violation,
Alan Kostelecky and Ralf Lehnert,
Phys. Rev. D 63, 065008 (2001).
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26. Analytical Construction of a Nonperturbative Vacuum for the Open Bosonic String,
Alan Kostelecky and Robertus Potting,
Phys. Rev. D 63, 046007 (2001).
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25. Limit on Lorentz and CPT Violation of the Neutron using a Two-Species Noble-Gas Maser,
David Bear, Richard Stoner, Ronald Walsworth, Alan Kostelecky, and Charles Lane,
Phys. Rev. Lett. 85, 5038 (2000).
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24. Off-Shell Structure of the String Sigma Model,
Alan Kostelecky, Malcolm Perry, and Robertus Potting,
Phys. Rev. Lett. 84, 4541 (2000).
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23. Lorentz and CPT Tests with Spin-Polarized Solids,
Robert Bluhm and Alan Kostelecky,
Phys. Rev. Lett. 84, 1381 (2000).
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22. CPT and Lorentz Tests with Muons,
Robert Bluhm, Alan Kostelecky, and Charles Lane,
Phys. Rev. Lett. 84, 1098 (2000).
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21. Signals for CPT and Lorentz Violation in Neutral-Meson Oscillations,
Alan Kostelecky,
Phys. Rev. D 61, 016002 (2000).
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20. Constraints on Lorentz Violation from Clock-Comparison Experiments,
Alan Kostelecky and Charles Lane,
Phys. Rev. D 60, 116010 (1999).
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19. Nonrelativistic Quantum Hamiltonian for Lorentz Violation,
Alan Kostelecky and Charles Lane,
J. Math. Phys. 40, 6245 (1999).
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18. Radiatively Induced Lorentz and CPT Violation in Electrodynamics,
Roman Jackiw and Alan Kostelecky,
Phys. Rev. Lett. 82, 3572 (1999).
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17. CPT and Lorentz Tests in Hydrogen and Antihydrogen,
Robert Bluhm, Alan Kostelecky, and Neil Russell,
Phys. Rev. Lett. 82, 2254 (1999).
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16. Lorentz-Violating Extension of the Standard Model,
Don Colladay and Alan Kostelecky,
Phys. Rev. D 58, 116002 (1998).
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15. CPT and Lorentz Tests in Penning Traps,
Robert Bluhm, Alan Kostelecky, and Neil Russell,
Phys. Rev. D 57, 3932 (1998).
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14. Sensitivity of CPT Tests with Neutral Mesons,
Alan Kostelecky,
Phys. Rev. Lett. 80, 1818 (1998).
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13. Testing CPT with Anomalous Magnetic Moments,
Robert Bluhm, Alan Kostelecky, and Neil Russell,
Phys. Rev. Lett. 79, 1432 (1997).
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12. CPT Violation and the Standard Model,
Don Colladay and Alan Kostelecky,
Phys. Rev. D 55, 6760 (1997).
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11. CPT Violation and Baryogenesis,
Orfeu Bertolami, Don Colladay, Alan Kostelecky, and Robertus Potting,
Phys. Lett. B 395, 178 (1997).
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10. Bounding CPT Violation in the Neutral-B System,
Alan Kostelecky and Rick Van Kooten,
Phys. Rev. D 54, 5585 (1996).
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9. Expectation Values, Lorentz Invariance, and CPT in the Open Bosonic String,
Alan Kostelecky and Robertus Potting,
Phys. Lett. B 381, 89 (1996).
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8. Testing CPT Invariance with the Neutral-D System,
Don Colladay and Alan Kostelecky,
Phys. Rev. D 52, 6224 (1995).
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7. Tests of Direct and Indirect CPT Violation at a B Factory,
Don Colladay and Alan Kostelecky,
Phys. Lett. B 344, 259 (1995).
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6. CPT, Strings, and Meson Factories,
Alan Kostelecky and Robertus Potting,
Phys. Rev. D 51, 3923 (1995).
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5. Photon and Graviton Masses in String Theories,
Alan Kostelecky and Stuart Samuel,
Phys. Rev. Lett. 66, 1811 (1991).
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4. CPT and Strings,
Alan Kostelecky and Robertus Potting,
Nucl. Phys. B 359, 545 (1991).
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3. Phenomenological Gravitational Constraints on Strings and Higher-Dimensional Theories,
Alan Kostelecky and Stuart Samuel,
Phys. Rev. Lett. 63, 224 (1989).
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2. Gravitational Phenomenology in Higher-Dimensional Theories and Strings,
Alan Kostelecky and Stuart Samuel,
Phys. Rev. D 40, 1886 (1989).
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1. Spontaneous Breaking of Lorentz Symmetry in String Theory,
Alan Kostelecky and Stuart Samuel,
Phys. Rev. D 39, 683 (1989).
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4. Nuclear Null Tests for Spacelike Neutrinos,
Alan Chodos and Alan Kostelecky,
Phys. Lett. B 336, 295 (1994).
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3. Mass Bounds for Spacelike Neutrinos,
Alan Kostelecky,
Topics in Quantum Gravity and Beyond: Essays in Honor of Louis Witten,
F. Mansouri and J.J. Scanio, eds., World Scientific, Singapore, 1993, p. 369-376.
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2. Null Experiments for Neutrino Masses,
Alan Chodos, Alan Kostelecky, Robertus Potting, and Evalyn Gates
Mod. Phys. Lett. A 7, 467 (1992).
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1. The Neutrino as a Tachyon,
Alan Chodos, Avi Hauser, and Alan Kostelecky,
Phys. Lett. B 150, 431 (1985).
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