Testing Lorentz invariance by the use of vacuum and matter filled cavity resonators

We consider tests of Lorentz invariance for the photon and fermion sector that use vacuum and matter-filled cavities. Assumptions on the wave function of the electrons in crystals are eliminated from the underlying theory and accurate sensitivity coefficients (including some exceptionally large ones) are calculated for various materials. We derive the Lorentz-violating shift in the index of refraction n, which leads to additional sensitivity for matter-filled cavities; and to birefringence in initially isotropic media. Using published experimental data, we obtain improved bounds on Lorentz violation for photons and electrons at levels of 10^-15 and below. We discuss implications for future experiments and propose a new Michelson-Morley--type experiment based on birefringence in matter.