The BPHZL renormalization method reveals ultraviolet and infrared finiteness in massless quantum electrodynamics, indicating model stability.
A bstract The renormalization of a parity-even massless U(1) × 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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Azevedo et al. (2025) studied this question.
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