An infinite-dimensional calculus for gauge theories

TL;DR

This paper develops an infinite-dimensional calculus framework for gauge theories using projective limits, enabling the rigorous definition of measures, functions, and operators in the space of gauge fields.

Contribution

It introduces a novel projective gauge triplet framework that extends calculus to infinite-dimensional gauge theory spaces, including measure behavior on nongeneric strata.

Findings

Defined gauge measures on nongeneric strata.

Constructed a projective gauge triplet for calculus.

Established a framework for infinite-dimensional gauge analysis.

Abstract

A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions and operators. From projective limits of test functions and distributions on products of compact groups, a projective gauge triplet is obtained, which provides a framework for the infinite-dimensional calculus in gauge theories. The gauge measure behavior on nongeneric strata is also obtained.