Quantum parity conservation in planar quantum electrodynamics

Abstract

Quantum parity conservation is verified at all orders in perturbation theory for a massless parityeven U (1) × U (1) planar quantum electrodynamics (QED3) model. The presence of two massless fermions requires the Lowenstein-Zimmermann (LZ) subtraction scheme, in the framework of the Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method, in order to subtract the infrared divergences induced by the ultraviolet subtractions at 1-and 2-loops, however thanks to the superrenormalizability of the model the ultraviolet divergences are bounded up to 2loops. Finally, it is proved that the BPHZL renormalization method preserves parity for the model taken into consideration, contrary to what happens to the ordinary massless parity-even U (1) QED3.