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arXiv · 2503.20012

The BPHZL renormalization of a planar quantum electrodynamics up to 2-loops and beyond

D. O. R. Azevedo·O. M. Del Cima·L. S. Lima·E. S. Miranda
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Abstract

The renormalization of a parity-even massless $U(1)\times U(1)$ quantum electrodynamics in three space-time dimensions (QED$_3$) is studied by adopting the Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method. The presence of two massless fermions requires the Lowenstein-Zimmermann (LZ) subtraction scheme to renormalize the infrared divergences induced by the ultraviolet subtractions at 1- and 2-loops, moreover due to the model superrenormalizability the ultraviolet divergences are bounded up to 2-loops. Finally, through the BPHZL renormalization method together with the LZ subtraction scheme the ultraviolet and infrared finiteness of the model is proved up to 2-loops and beyond.

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D. O. R. Azevedo, O. M. Del Cima, L. S. Lima, E. S. Miranda. 2025-03-25. The BPHZL renormalization of a planar quantum electrodynamics up to 2-loops and beyond. https://doi.org/10.1007/jhep07(2025)183

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