  In this work we outline the two most commonly used test theories (RMS and
SME) for testing Local Lorentz Invariance (LLI) of the photon. Then we develop
the general framework of applying these test theories to resonator experiments
with an emphasis on rotating experiments in the laboratory. We compare the
inherent sensitivity factors of common experiments and propose some new
configurations. Finally we apply the test theories to the rotating cryogenic
experiment at the University of Western Australia, which recently set new
limits in both the RMS and SME frameworks [hep-ph/0506074].
