  The aim of this brief review is to present a case study of how astrophysics
data can be used to get bounds on Lorentz-violating parameters. For this
purpose, a particularly simple Lorentz-violating modification of the Maxwell
theory of photons is considered, which maintains gauge invariance, CPT, and
renormalization. With a standard spin-one-half Dirac particle minimally coupled
to this nonstandard photon, the resulting modified-quantum-electrodynamics
model involves nineteen dimensionless "deformation parameters." Ten of these
parameters lead to birefringence and are already tightly constrained by
astrophysics. New bounds on the remaining nine nonbirefringent parameters have
been obtained from the inferred absence of vacuum Cherenkov radiation in
ultrahigh-energy-cosmic-ray (UHECR) events. The resulting astrophysics bounds
improve considerably upon current laboratory bounds and the implications of
this "null experiment" may be profound, both for elementary particle physics
and cosmology.
