Modern Tests of Lorentz Invariance David Mattingly Department of Physics University of California at Davis Davis, CA 95616, U.S.A. email: mattingly@physics.ucdavis.edu http://lifshitz.ucdavis.edu/~mattingly Accepted on 4 July 2005 Published on 7 September 2005 Living Reviews in Relativity Published by the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1, 14424 Golm, Germany ISSN 1433-8351 Abstract Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented. How to cite this article Owing to the fact that a Living Reviews article can evolve over time, we recommend to cite the article as follows: David Mattingly, “Modern Tests of Lorentz Invariance”. Living Rev. Relativity, 8, (2005), 5. [Online Article]: cited <date>, http://www.livingreviews.org/lrr-2005-5 The date given as <date> then uniquely identifies the version of the article you are referring to. Article Revisions Living Reviews supports two different ways to keep its articles up-to-date: Fast-track revision A fast-track revision provides the author with the opportunity to add short notices of current research results, trends and developments, or important publications to the article. A fast-track revision is refereed by the responsible subject editor. If an article has undergone a fast-track revision, a summary of changes will be listed here. Major update A major update will include substantial changes and additions and is subject to full external refereeing. It is published with a new publication number. For detailed documentation of an article’s evolution, please refer always to the history document of the article’s online version at http://www.livingreviews.org/lrr-2005-5. Contents 1 Introduction 5 2 General Considerations 7 2.1 Defining Lorentz violation 7 2.1.1 Lorentz violation in field theory 7 2.1.2 Modified Lorentz groups 8 2.2 Kinematics vs. dynamics 8 2.3 The role of other symmetries 8 2.3.1 CPT invariance 9 2.3.2 Supersymmetry 9 2.3.Modern Tests of Lorentz Invariance David Mattingly Department of Physics University of California at Davis Davis, CA 95616, U.S.A. email: mattingly@physics.ucdavis.edu http://lifshitz.ucdavis.edu/~mattingly Accepted on 4 July 2005 Published on 7 September 2005 Living Reviews in Relativity Published by the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1, 14424 Golm, Germany ISSN 1433-8351 Abstract Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented. How to cite this article Owing to the fact that a Living Reviews article can evolve over time, we recommend to cite the article as follows: David Mattingly, “Modern Tests of Lorentz Invariance”. Living Rev. Relativity, 8, (2005), 5. [Online Article]: cited <date>, http://www.livingreviews.org/lrr-2005-5 The date given as <date> then uniquely identifies the version of the article you are referring to. Article Revisions Living Reviews supports two different ways to keep its articles up-to-date: Fast-track revision A fast-track revision provides the author with the opportunity to add short notices of current research results, trends and developments, or important publications to the article. A fast-track revision is refereed by the responsible subject editor. If an article has undergone a fast-track revision, a summary of changes will be listed here. Major update A major update will include substantial changes and additions and is subject to full external refereeing. It is published with a new publication number. For detailed documentation of an article’s evolution, please refer always to the history document of the article’s online version at http://www.livingreviews.org/lrr-2005-5. Contents 1 Introduction 5 2 General Considerations 7 2.1 Defining Lorentz violation 7 2.1.1 Lorentz violation in field theory 7 2.1.2 Modified Lorentz groups 8 2.2 Kinematics vs. dynamics 8 2.3 The role of other symmetries 8 2.3.1 CPT invariance 9 2.3.2 Supersymmetry 9 2.3.