A reparametrization invariant surface ordering

TL;DR

This paper introduces a reparametrization invariant non-Abelian Wilson surface on loop space, utilizing a novel tensor product representation of the Lie algebra to define gauge fields and surface ordering.

Contribution

It presents a new reparametrization invariant surface ordering framework using an infinite-dimensional tensor product Lie algebra representation.

Findings

Defined a non-Abelian Wilson surface as a time-ordered exponential

Established reparametrization invariance of the Wilson surface

Developed a suitable tensor product representation for loop space fields

Abstract

We introduce a notion of a non-Abelian loop gauge field defined on points in loop space. For this purpose we first find an infinite-dimensional tensor product representation of the Lie algebra which is particularly suited for fields on loop space. We define the non-Abelian Wilson surface as a `time' ordered exponential in terms of this loop gauge field and show that it is reparametrization invariant.