Quantum parity conservation in planar quantum electrodynamics

TL;DR

This paper proves that quantum parity is conserved at all orders in a specific massless planar QED$_3$ model, demonstrating the effectiveness of the BPHZL renormalization scheme in preserving symmetry.

Contribution

It shows that BPHZL renormalization preserves parity in massless parity-even U(1) QED$_3$, unlike in the standard case, and addresses infrared divergence subtraction.

Findings

Parity is conserved at all perturbative orders.

BPHZL renormalization preserves parity in the model.

Infrared divergences are successfully subtracted using LZ scheme.

Abstract

Quantum parity conservation is verified at all orders in perturbation theory for a massless parity-even $U(1)\times U(1)$ planar quantum electrodynamics (QED$_3$) 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 2-loops. 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 $U(1)$ QED$_3$.