Amenability of the Gauge Group

TL;DR

The paper investigates the amenability of local gauge groups with a focus on a coarser topology that makes these groups amenable and more useful for mathematical and physical applications.

Contribution

It introduces a new, coarser topology on gauge groups that ensures their amenability and demonstrates its usefulness in a fermionic model.

Findings

Gauge groups are amenable under a specific coarser topology.

The new topology is more practical than previously known amenable topologies.

A fermionic model with continuous gauge group action is constructed.

Abstract

Let G be one of the local gauge groups C(X,U(n)), C^\infty(X,U(n)), C(X,SU(n)) or C^\infty(X,SU(n)) where X is a compact Riemannian manifold. We observe that G has a nontrivial group topology, coarser than its natural topology, w.r.t. which it is amenable, viz the relative weak topology of C(X,M(n)). This topology seems more useful than other known amenable topologies for G. We construct a simple fermionic model containing an action of G, continuous w.r.t. this amenable topology.