Living Reviews in Relativity

"Modern Tests of Lorentz Invariance"
by
David Mattingly  

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Abstract
1 Introduction
2 General Considerations
2.1 Defining Lorentz violation
2.2 Kinematics vs. dynamics
2.3 The role of other symmetries
2.4 Diffeomorphism invariance and prior geometry
2.5 Lorentz violation and the equivalence principle
2.6 Systematic vs. non-systematic violations
2.7 Causality and stability
3 Kinematic Frameworks for Lorentz Violation
3.1 Systematic modified dispersion
3.2 Robertson-Mansouri-Sexl framework
3.3 c-squared framework
3.4 “Doubly special” relativity
3.5 Non-systematic dispersion
4 Dynamical Frameworks for Lorentz Violation
4.1 Effective field theory
4.2 Non-commutative spacetime
4.3 Symmetry and relevant/irrelevant Lorentz violating operators
4.4 Lorentz violation with gravity in EFT
5 Terrestrial Constraints on Lorentz Violation
5.1 Penning traps
5.2 Clock comparison experiments
5.3 Cavity experiments
5.4 Spin polarized torsion balances
5.5 Neutral mesons
5.6 Doppler shift of lithium
5.7 Muon experiments
5.8 Constraints on the Higgs sector
6 Astrophysical Constraints on Lorentz Violation
6.1 Relevance of astrophysical observations
6.2 Time of flight
6.3 Birefringence
6.4 Threshold constraints
6.5 Particle threshold interactions in EFT
6.6 Threshold reactions in other models
6.7 Synchrotron radiation
6.8 Neutrinos
6.9 Phase coherence of light
7 Gravitational Observations
7.1 Gravitational waves
7.2 Cosmology
7.3 PPN parameters
8 Conclusions and Prospects
9 Acknowledgements
Open References References
Footnotes
Figures