We determine limits from SN 1987A on massive axion-like particles with masses in the 10 keV -100 MeV range and purely coupled to two photons. Axion-like particles produced in the core collapse escape from the star and decay into photons that can be observed as a delayed and diffuse burst. We discuss the time and angular distribution of such a signal. Looking into the future we also estimate the possible improvements caused by better gamma-ray detectors or if the red supergiant Betelgeuse explodes in a supernova event.

We determine the effect of a CPT-even and Lorentz violating non-minimal coupling on the differential cross sections for some of the most important tree-level processes in QED, namely, Compton and Bhabha scatterings, as well as electron-positron annihilation. Experimental limits constraining the allowed deviation of the differential cross sections relative to pure QED allow us to place upper bounds on the Lorentz violating parameters. A constraint based on the decay rate of parapositronium is also obtained.

The CPT-odd and Lorentz-violating Carroll-Field-Jackiw modification of electrodynamics is discussed and we study its effects on the energy spectrum of hydrogen, as well as in the generation of a momentum-dependent electric dipole moment for charged leptons. We also briefly comment on the possibility of the detection of Lorentz violation in measurements of vacuum birefringence in resonant cavities. The bounds found are based on local laboratory experimental limits and are not competitive with the ones coming from astrophysical considerations.