  There is a unique Lorentz-violating modification of the Maxwell theory of
photons, which maintains gauge invariance, CPT, and renormalizability.
Restricting the modified-Maxwell theory to the isotropic sector and adding a
standard spin-one-half Dirac particle p^\pm with minimal coupling to the
nonstandard photon \widetilde{\gamma}, the resulting
modified-quantum-electrodynamics model involves a single dimensionless
"deformation parameter," \widetilde{\kappa}_{tr}. The exact tree-level decay
rates for two processes have been calculated: vacuum Cherenkov radiation p^\pm
\to p^\pm \widetilde{\gamma} for the case of positive \widetilde{\kappa}_{tr}
and photon decay \widetilde{\gamma} \to p^+ p^- for the case of negative
\widetilde{\kappa}_{tr}. From the inferred absence of these decays for a
particular high-quality ultrahigh-energy-cosmic-ray event detected at the
Pierre Auger Observatory and an excess of TeV gamma-ray events observed by the
High Energy Stereoscopic System telescopes, a two-sided bound on
\widetilde{\kappa}_{tr} is obtained, which improves by eight orders of
magnitude upon the best direct laboratory bound. The implications of this
result are briefly discussed.
