Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids

TL;DR

This paper reveals a BRS symmetry in the path integral formulation of randomly stirred fluids, analogous to gauge symmetry in quantum field theory, and derives related identities to ensure consistency of correlation functions.

Contribution

It introduces a gauge fixing procedure respecting BRS symmetry in fluid dynamics, establishing Slavnov-Taylor-like identities for correlation functions.

Findings

BRS symmetry exists in the path integral for randomly stirred fluids.

A gauge fixing procedure preserves BRS symmetry.

Derived identities ensure consistent correlation functions.

Abstract

The path integral for randomly forced incompressible fluids is shown to have an underlying Becchi-Rouet-Stora (BRS) symmetry as a consequence of Galilean invariance. This symmetry must be respected to have a consistent generating functional, free from both an overall infinite factor and spurious relations amongst correlation functions. We present a procedure for respecting this BRS symmetry, akin to gauge fixing in quantum field theory. Relations are derived between correlation functions of this gauge fixed, BRS symmetric theory, analogous to the Slavnov-Taylor identities of quantum field theory.