Stochastic quantization of an Abelian gauge theory

Abstract

We study the Langevin dynamics of a U(1) lattice gauge theory on the torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by space-time white noises. This also yields convergence of some gauge invariant observables on a short time interval. We fix gauge via a DeTurck trick, and prove a version of Ward identity which results in cancellation of renormalization constants that would otherwise break gauge symmetry. The proof relies on a discrete version of the theory of regularity structures.

67 pages, rewrote and improved some of the proofs

References in corpus (3)

• Renormalising SPDEs in regularity structures
• Geometric stochastic heat equations
• The dynamical sine-Gordon model in the full subcritical regime

Cited by in corpus (1)

• Some recent progress in singular stochastic PDEs