Galilean fermions: Classical and quantum aspects

TL;DR

This paper explores the classical and quantum properties of Galilean fermions in 3+1 dimensions, revealing their invariance under infinite conformal symmetries classically, but showing symmetry breaking at the quantum level with the emergence of a mass scale.

Contribution

It introduces a minimally coupled massless Galilean fermion theory in 3+1 dimensions, demonstrating its classical conformal invariance and quantum renormalizability, along with symmetry breaking at the quantum level.

Findings

Classical theory exhibits infinite Galilean conformal symmetry.

Quantum corrections induce a mass scale and break conformal symmetry.

The theory is renormalizable at the quantum level.

Abstract

We study the classical and quantum "properties" of Galilean fermions in 3+1 dimensions. We have taken the case of massless Galilean fermions minimally coupled to the scalar field. At the classical level, the Lagrangian is obtained by null reducing the relativistic theory in one higher dimension. The resulting theory is found to be invariant under infinite Galilean conformal symmetries. Using Noether's procedure, we construct the corresponding infinite conserved charges. Path integral techniques are then employed to probe the quantum "properties" of the theory. The theory is found to be renormalizable. A novel feature of the theory is the emergence of mass scale at the first order of quantum correction. The conformal symmetry of the theory breaks at the quantum level. We confirm this by constructing the beta function of the theory.