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

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.

References in corpus (8)

• Landau Level Splitting in Graphene in High Magnetic Fields
• The zero-energy state in graphene in a high magnetic field
• Chiral Gauge Theory for Graphene
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• No parity anomaly in massless QED3: a BPHZL approach
• The quantum scale invariance in graphene-like quantum electrodynamics
• Quantum parity conservation in planar quantum electrodynamics
• Critical properties of three-dimensional many-flavour QEDs