Quantization of Interacting Galilean Field theories

TL;DR

This paper develops a quantum field theory for Galilean electrodynamics coupled with massless fermions, derived from a higher-dimensional relativistic theory, and analyzes its quantum corrections and renormalizability.

Contribution

It introduces a quantum field description of Galilean electrodynamics with fermions, derived via null reduction, and investigates its renormalization properties and beta function behavior.

Findings

Quantum corrections to propagators and vertices calculated up to first order.

The theory is renormalizable at this order.

The beta function grows linearly, indicating non-asymptotic freedom.

Abstract

We present the quantum field description of Galilean electrodynamics minimally coupled to massless Galilean fermion in (3 + 1) dimensions. At the classical level, the Lagrangian is obtained as a null reduction of a relativistic theory in one higher dimension. We use functional techniques to develop the quantum field description of the theory. Quantum corrections to the propagators and vertex are obtained upto first order and the theory is found to be renormalizable to this order. The beta function of the theory is found to grow linearly; the theory is not asymptotically free.