Lorentz invariance, the fundamental symmetry of Einstein's theory of Special
Relativity, has been established and tested by many classical and modern
experiments. However, many theories that unify the Standard Model of particle
physics and General Relativity predict a violation of Lorentz invariance at the
Planck scale. While this energy range cannot be reached by current experiments,
minute deviations from Lorentz symmetry may be present at lower energies.
Astrophysical experiments are very suitable to search for these deviations,
since their effects accumulate as photons travel across large distances. In
this paper, we describe astrophysical methods that we used to constrain the
photon dispersion and vacuum birefringence.