Manifestly gauge invariant exact renormalization group for quantum electrodynamics

DOI10.1093/PTEP/PTAC003zbMATH Open1487.81149arXiv2111.15529OpenAlexW4205099285MaRDI QIDQ3390517

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Publication date: 24 March 2022

Published in: PTEP. Progress of Theoretical and Experimental Physics (Search for Journal in Brave)

Abstract: We formulate quantum electrodynamics on the basis of gauge (or BRST) covariant diffusion equations of fields. This is a particular example of the gradient flow exact renormalization group (GFERG). The resulting Wilson action fulfills a simple gauge Ward--Takahashi identity. We solve the GFERG equation around the Gaussian fixed point to the second order in gauge coupling and obtain the 1-loop beta function and anomalous dimensions. The anomalous dimension of the electron field coincides with that of the fermion field diffused by a gauge covariant flow equation of L"uscher.

Full work available at URL: https://arxiv.org/abs/2111.15529

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Yang-Mills and other gauge theories in quantum field theory (81T13) Electromagnetic interaction; quantum electrodynamics (81V10) Renormalization group methods applied to problems in quantum field theory (81T17) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15) Fermionic systems in quantum theory (81V74)