This work tabulates measured and derived values of coefficients for Lorentz and CPT violation in the Standard-Model Extension. Summary tables are extracted listing maximal attained sensitivities in the matter, photon, neutrino, and gravity sectors. T
ables presenting definitions and properties are also compiled.
Bipartite Riemann-Finsler geometries with complementary Finsler structures are constructed. Calculable examples are presented based on a bilinear-form coefficient for explicit Lorentz violation.
Classical point-particle relativistic lagrangians are constructed that generate the momentum-velocity and dispersion relations for quantum wave packets in Lorentz-violating effective field theory.
A general framework for tests of Lorentz invariance with electromagnetic waves is presented, allowing for operators of arbitrary mass dimension. Signatures of Lorentz violations include vacuum birefringence, vacuum dispersion, and anisotropies. Sensi
tive searches for violations using sources such as active galaxies, gamma-ray bursts, and the cosmic microwave background are discussed. Direction-dependent dispersion constraints are obtained on operators of dimension 6 and 8 using gamma-ray bursts and the blazar Markarian 501. Stringent constraints on operators of dimension 3 are found using 5-year data from the Wilkinson Microwave Anisotropy Probe. No evidence appears for isotropic Lorentz violation, while some support at one sigma is found for anisotropic violation.
Deviations from relativity are tightly constrained by numerous experiments. A class of unmeasured and potentially large violations is presented that can be tested in the laboratory only via weak gravity couplings. Specialized highly sensitive experim
ents could achieve measurements of the corresponding effects. A single constraint of 1 x 10^{-11} GeV is extracted on one combination of the 12 possible effects in ordinary matter. Estimates are provided for attainable sensitivities in existing and future experiments.
Exceptional sensitivity to spacetime torsion can be achieved by searching for its couplings to fermions. Recent experimental searches for Lorentz violation are exploited to extract new constraints involving 19 of the 24 independent torsion components down to levels of order 10^{-31} GeV.
This talk offers some comments and perspectives on Lorentz and CPT violation.
