Background information on

LORENTZ  AND  CPT  VIOLATION


Web page last updated November 15, 2014

Our basic premise is that minuscule apparent violations of Lorentz and CPT invariance might be observable in nature. The idea is that the violations would arise as suppressed effects from a more fundamental theory.

We have shown in our publications that arbitrary Lorentz and CPT violations are quantitatively described by a theory called the Standard-Model Extension (SME), which is a modification of the usual Standard Model of particle physics and Einstein's theory of gravity, General Relativity.

This web page contains:

  • media coverage
  • questions and answers about Lorentz and CPT violation
  • partial bibliography of experimental results
  • partial bibliography of theoretical results for Lorentz and CPT violation and for tachyonic neutrinos

    Related items:

  • Beyond Einstein: the Search for Relativity Violations (lay description of our research program, streaming video, 7 min)
  • animations of some of our results
  • Posters summarizing the 2013 Data Tables for Lorentz and CPT Violation: first poster, second poster
  • INSPIRE partial listings for Lorentz and CPT violation and for superluminal neutrinos
  • The Indiana University Center for Spacetime Symmetries (IUCSS)

    Upcoming meetings:

  • SME 2015 summer school
  • Past meetings:

  • CPT'13 CPT'10, CPT'07, CPT'04, CPT'01, and CPT'98 conferences
  • LVGR'14 workshop
  • LVG'12 workshop
  • SME 2012 summer school
  • LVNU'12 workshop
  • SME 2011 workshop

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    FREQUENTLY ASKED QUESTIONS

    What is Lorentz and CPT symmetry?

    What is the CPT theorem?

    What are we doing and why?

    What is the Standard Model and what is the Standard-Model Extension?

    How does CPT violation differ from violations of C, P, T, CP?

    What could cause Lorentz and CPT violation?

    What are the properties of the Standard-Model Extension?

    Which experiments can test these ideas and which provide the best tests?


    ANSWERS TO THE QUESTIONS

    What is Lorentz and CPT symmetry?

    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.

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

    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.

    What is the CPT theorem?

    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). 


    What are we doing and why?

    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.


    What is the Standard Model and what is the Standard-Model Extension?

    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) (the archived preprint is available).


    How does CPT violation differ from violations of C, P, T, CP?

    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.

    What could cause Lorentz and CPT violation?

    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.


    What are the properties of the Standard-Model Extension?

    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.

    Which experiments can test these ideas and which provide the best tests?

    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:

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

    Experimental measurements of coefficients for Lorentz and CPT violation in the Standard-Model Extension include those described in the following references. A compilation of experimental results can be found in the Data Tables for Lorentz and CPT Violation, paper 56 in the bibliography.


    BIBLIOGRAPHY

    Books

    CPT and Lorentz Symmetry VI, Alan Kostelecky, ed. (World Scientific, Singapore, 2014).

    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).


    Articles on Lorentz and CPT violation

    77. Short-Range Gravity and Lorentz Violation,
    Quentin Bailey, Alan Kostelecky, and Rui Xu,
    submitted for publication.
    The archived preprint is available.

    76. Laboratory Tests of Lorentz and CPT Symmetry with Muons,
    Andre Gomes, Alan Kostelecky, and Arnaldo Vargas,
    Phys. Rev. D 90, 076009 (2014).
    The archived preprint is available.

    75. Testing Relativity with High-Energy Astrophysical Neutrinos,
    Jorge Diaz, Alan Kostelecky, and Matthew Mewes,
    Phys. Rev. D 89, 043005 (2014).
    The archived preprint is available.

    74. Fermions with Lorentz-Violating Operators of Arbitrary Dimension,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. D 88, 096006 (2013).
    The archived preprint is available.

    73. Relativity Violations and Beta Decay,
    Jorge Diaz, Alan Kostelecky, and Ralf Lehnert,
    Phys. Rev. D 88, 071902(R) (2013).
    The archived preprint is available.

    72. Constraints on Relativity Violations from Gamma-Ray Bursts,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. Lett. 110, 201601 (2013).
    The archived preprint is available.

    71. Bipartite Riemann-Finsler Geometry and Lorentz Violation,
    Alan Kostelecky, Neil Russell, and Rhondale Tso,
    Phys. Lett. B 716, 470 (2012).
    The archived preprint is available.

    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).
    The archived preprint is available.

    69. Neutrinos with Lorentz-Violating Operators of Arbitrary Dimension,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. D 85, 096005 (2012).
    The archived preprint is available.

    68. Lorentz- and CPT-Violating Models for Neutrino Oscillations,
    Jorge Diaz and Alan Kostelecky,
    Phys. Rev. D 85, 016013 (2012).
    The archived preprint is available.

    67. Riemann-Finsler Geometry and Lorentz-Violating Kinematics,
    Alan Kostelecky,
    Phys. Lett. B 701, 137 (2011).
    The archived preprint is available.

    66. Three-parameter Lorentz-Violating Texture for Neutrino Mixing,
    Jorge Diaz and Alan Kostelecky,
    Phys. Lett. B 700, 25 (2011).
    The archived preprint is available.

    65. Classical Kinematics for Lorentz Violation,
    Alan Kostelecky and Neil Russell,
    Phys. Lett. B 693, 443 (2010).
    The archived preprint is available.

    64. CPT Violation and B-Meson Oscillations,
    Alan Kostelecky and Rick Van Kooten,
    Phys. Rev. D 82, 101702(R) (2010).
    The archived preprint is available.

    63. Matter-Gravity Couplings and Lorentz Violation,
    Alan Kostelecky and Jay Tasson,
    Phys. Rev. D 83, 016013 (2011).
    The archived preprint is available.

    62. Lorentz Violation with an Antisymmetric Tensor,
    Brett Altschul, Quentin Bailey, and Alan Kostelecky,
    Phys. Rev. D 81, 065028 (2010).
    The archived preprint is available.

    61. Perturbative Lorentz and CPT Violation for Neutrino and Antineutrino Oscillations,
    Jorge Diaz, Alan Kostelecky, and Matthew Mewes,
    Phys. Rev. D 80, 076007 (2009).
    The archived preprint is available.

    60. Electrodynamics with Lorentz-Violating Operators of Arbitrary Dimension,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. D 80, 015020 (2009).
    The archived preprint is available.

    59. Gravity from Spontaneous Lorentz Violation,
    Alan Kostelecky and Robertus Potting,
    Phys. Rev. D 79, 065018 (2009).
    The archived preprint is available.

    58. Prospects for Large Relativity Violations in Matter-Gravity Couplings,
    Alan Kostelecky and Jay Tasson,
    Phys. Rev. Lett. 102, 010402 (2009).
    The archived preprint is available.

    57. Astrophysical Tests of Lorentz and CPT Violation with Photons,
    Alan Kostelecky and Matthew Mewes,
    Astrophys. J. Lett. 689, L1 (2008).
    The archived preprint is available.

    56. Data Tables for Lorentz and CPT Violation,
    Alan Kostelecky and Neil Russell,
    Rev. Mod. Phys. 83, 11 (2011).
    The archived preprint is available.

    55. New Constraints on Torsion from Lorentz Violation,
    Alan Kostelecky, Neil Russell, and Jay Tasson,
    Phys. Rev. Lett. 100, 111102 (2008).
    The archived preprint is available.

    54. Spontaneous Lorentz and Diffeomorphism Violation, Massive Modes, and Gravity,
    Robert Bluhm, Shu-Hong Fung, and Alan Kostelecky,
    Phys. Rev. D 77, 065020 (2008).
    The archived preprint is available.

    53. Lorentz-Violating Electrodynamics and the Cosmic Microwave Background,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. Lett. 99, 011601 (2007).
    The archived preprint is available.

    52. Sensitive Polarimetric Search for Relativity Violations in Gamma-Ray Bursts,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. Lett. 97, 140401 (2006).
    The archived preprint is available.

    51. Global Three-Parameter Model for Neutrino Oscillations using Lorentz Violation,
    Teppei Katori, Alan Kostelecky, and Rex Tayloe,
    Phys. Rev. D 74, 105009 (2006).
    The archived preprint is available.

    50. Signals for Lorentz Violation in Post-Newtonian Gravity,
    Quentin Bailey and Alan Kostelecky,
    Phys. Rev. D 74, 045001 (2006).
    The archived preprint is available.

    49. Gravity from Local Lorentz Violation,
    Alan Kostelecky and Robertus Potting,
    Gen. Rel. Grav. 37, 1675 (2005).
    The archived preprint is available.

    48. Spontaneous Lorentz Violation and Nonpolynomial Interactions,
    Brett Altschul and Alan Kostelecky,
    Phys. Lett. B 628, 106 (2005).
    The archived preprint is available.

    47. Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity,
    Robert Bluhm and Alan Kostelecky,
    Phys. Rev. D 71, 065008 (2005).
    The archived preprint is available.

    46. Lorentz-Violating Electrostatics and Magnetostatics,
    Quentin Bailey and Alan Kostelecky,
    Phys. Rev. D 70, 076006 (2004).
    The archived preprint is available.

    45. Lorentz Violation and Short-Baseline Neutrino Experiments,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. D 70, 076002 (2004).
    The archived preprint is available.

    44. Gravity, Lorentz Violation, and the Standard Model,
    Alan Kostelecky,
    Phys. Rev. D 69, 105009 (2004).
    The archived preprint is available.

    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).
    The archived preprint is available.

    42. Lorentz and CPT Violation in Neutrinos,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. D 69, 016005 (2004).
    The archived preprint is available.

    41. Lorentz and CPT Violation in the Neutrino Sector,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. D 70, 031902(R) (2004).
    The archived preprint is available.

    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).
    The archived preprint is available.

    39. Vacuum Photon Splitting in Lorentz-Violating Quantum Electrodynamics,
    Alan Kostelecky and Austin Pickering,
    Phys. Rev. Lett. 91, 031801 (2003).
    The archived preprint is available.

    38. Spacetime Varying Couplings and Lorentz Violation,
    Alan Kostelecky, Ralf Lehnert, and Malcolm Perry,
    Phys. Rev. D 68, 123511 (2003).
    The archived preprint is available.

    37. Signals for Lorentz Violation in Electrodynamics,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. D 66, 056005 (2002).
    The archived preprint is available.

    36. Supersymmetry and Lorentz Violation,
    Micheal Berger and Alan Kostelecky,
    Phys. Rev. D 65, 091701(R) (2002).
    The archived preprint is available.

    35. One-Loop Renormalization of Lorentz-Violating Electrodynamics,
    Alan Kostelecky, Charles Lane, and Austin Pickering,
    Phys. Rev. D 65, 056006 (2002).
    The archived preprint is available.

    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).
    The archived preprint is available.

    33. Cosmological Constraints on Lorentz Violation in Electrodynamics,
    Alan Kostelecky and Matthew Mewes,
    Phys. Rev. Lett. 87, 251304 (2001).
    The archived preprint is available.

    32. Background Enhancement of CPT Reach at an Asymmetric Phi Factory,
    Nathan Isgur, Alan Kostelecky, and Adam Szczepaniak,
    Phys. Lett. B 515, 333 (2001).
    The archived preprint is available.

    31. Noncommutative Field Theory and Lorentz Violation,
    Sean Carroll, Jeffrey Harvey, Alan Kostelecky, Charles Lane, and Takemi Okamoto,
    Phys. Rev. Lett. 87, 141601 (2001).
    The archived preprint is available.

    30. Cross Sections and Lorentz Violation,
    Don Colladay and Alan Kostelecky,
    Phys. Lett. B 511, 209 (2001).
    The archived preprint is available.

    29. CPT, T, and Lorentz Violation in Neutral-Meson Oscillations,
    Alan Kostelecky,
    Phys. Rev. D 64, 076001 (2001).
    The archived preprint is available.

    28. Analogue Models for T and CPT Violation in Neutral-Meson Oscillations,
    Alan Kostelecky and Agnes Roberts,
    Phys. Rev. D 63, 096002 (2001).
    The archived preprint is available.

    27. Stability, Causality, and Lorentz and CPT Violation,
    Alan Kostelecky and Ralf Lehnert,
    Phys. Rev. D 63, 065008 (2001).
    The archived preprint is available.

    26. Analytical Construction of a Nonperturbative Vacuum for the Open Bosonic String,
    Alan Kostelecky and Robertus Potting,
    Phys. Rev. D 63, 046007 (2001).
    The archived preprint is available.

    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).
    The archived preprint is available.

    24. Off-Shell Structure of the String Sigma Model,
    Alan Kostelecky, Malcolm Perry, and Robertus Potting,
    Phys. Rev. Lett. 84, 4541 (2000).
    The archived preprint is available.

    23. Lorentz and CPT Tests with Spin-Polarized Solids,
    Robert Bluhm and Alan Kostelecky,
    Phys. Rev. Lett. 84, 1381 (2000).
    The archived preprint is available.

    22. CPT and Lorentz Tests with Muons,
    Robert Bluhm, Alan Kostelecky, and Charles Lane,
    Phys. Rev. Lett. 84, 1098 (2000).
    The archived preprint is available.

    21. Signals for CPT and Lorentz Violation in Neutral-Meson Oscillations,
    Alan Kostelecky,
    Phys. Rev. D 61, 016002 (2000).
    The archived preprint is available.

    20. Constraints on Lorentz Violation from Clock-Comparison Experiments,
    Alan Kostelecky and Charles Lane,
    Phys. Rev. D 60, 116010 (1999).
    The archived preprint is available.

    19. Nonrelativistic Quantum Hamiltonian for Lorentz Violation,
    Alan Kostelecky and Charles Lane,
    J. Math. Phys. 40, 6245 (1999).
    The archived preprint is available.

    18. Radiatively Induced Lorentz and CPT Violation in Electrodynamics,
    Roman Jackiw and Alan Kostelecky,
    Phys. Rev. Lett. 82, 3572 (1999).
    The archived preprint is available.

    17. CPT and Lorentz Tests in Hydrogen and Antihydrogen,
    Robert Bluhm, Alan Kostelecky, and Neil Russell,
    Phys. Rev. Lett. 82, 2254 (1999).
    The archived preprint is available.

    16. Lorentz-Violating Extension of the Standard Model,
    Don Colladay and Alan Kostelecky,
    Phys. Rev. D 58, 116002 (1998).
    The archived preprint is available.

    15. CPT and Lorentz Tests in Penning Traps,
    Robert Bluhm, Alan Kostelecky, and Neil Russell,
    Phys. Rev. D 57, 3932 (1998).
    The archived preprint is available.

    14. Sensitivity of CPT Tests with Neutral Mesons,
    Alan Kostelecky,
    Phys. Rev. Lett. 80, 1818 (1998).
    The archived preprint is available.

    13. Testing CPT with Anomalous Magnetic Moments,
    Robert Bluhm, Alan Kostelecky, and Neil Russell,
    Phys. Rev. Lett. 79, 1432 (1997).
    The archived preprint is available.

    12. CPT Violation and the Standard Model,
    Don Colladay and Alan Kostelecky,
    Phys. Rev. D 55, 6760 (1997).
    The archived preprint is available.

    11. CPT Violation and Baryogenesis,
    Orfeu Bertolami, Don Colladay, Alan Kostelecky, and Robertus Potting,
    Phys. Lett. B 395, 178 (1997).
    The archived preprint is available.

    10. Bounding CPT Violation in the Neutral-B System,
    Alan Kostelecky and Rick Van Kooten,
    Phys. Rev. D 54, 5585 (1996).
    The archived preprint is available.

    9. Expectation Values, Lorentz Invariance, and CPT in the Open Bosonic String,
    Alan Kostelecky and Robertus Potting,
    Phys. Lett. B 381, 89 (1996).
    The archived preprint is available.

    8. Testing CPT with the Neutral-D System,
    Don Colladay and Alan Kostelecky,
    Phys. Rev. D 52, 6224 (1995).
    The archived preprint is available.

    7. Tests of Direct and Indirect CPT Violation at a B Factory,
    Don Colladay and Alan Kostelecky,
    Phys. Lett. B 344, 259 (1995).
    The archived preprint is available.

    6. CPT, Strings, and Meson Factories,
    Alan Kostelecky and Robertus Potting,
    Phys. Rev. D 51, 3923 (1995).
    The archived preprint is available.

    5. Photon and Graviton Masses in String Theories,
    Alan Kostelecky and Stuart Samuel,
    Phys. Rev. Lett. 66, 1811 (1991).
    PRL server

    4. CPT and Strings,
    Alan Kostelecky and Robertus Potting,
    Nucl. Phys. B 359, 545 (1991).
    NPB server

    3. Phenomenological Gravitational Constraints on Strings and Higher-Dimensional Theories,
    Alan Kostelecky and Stuart Samuel,
    Phys. Rev. Lett. 63, 224 (1989).
    PRL server

    2. Gravitational Phenomenology in Higher-Dimensional Theories and Strings,
    Alan Kostelecky and Stuart Samuel,
    Phys. Rev. D 40, 1886 (1989).
    PRD server

    1. Spontaneous Breaking of Lorentz Symmetry in String Theory,
    Alan Kostelecky and Stuart Samuel,
    Phys. Rev. D 39, 683 (1989).
    PRD server


    Articles on tachyonic neutrinos

    4. Nuclear Null Tests for Spacelike Neutrinos,
    Alan Chodos and Alan Kostelecky,
    Phys. Lett. B 336, 295 (1994).
    The archived
    preprint is available.

    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.
    The preprint is available.

    2. Null Experiments for Neutrino Masses,
    Alan Chodos, Alan Kostelecky, Robertus Potting, and Evalyn Gates
    Mod. Phys. Lett. A 7, 467 (1992).
    MPLA server
    The preprint is available.

    1. The Neutrino as a Tachyon,
    Alan Chodos, Avi Hauser, and Alan Kostelecky,
    Phys. Lett. B 150, 431 (1985).
    PLB server
    The preprint is available.


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