Measure and mass gap for generalized connections on hypercubic lattices

TL;DR

This paper develops a mathematical framework for non-abelian generalized connections on hypercubic lattices, establishing a measure and calculus, and presents new results on the mass gap for compact structure groups.

Contribution

It introduces a consistent measure and calculus for non-abelian connections on lattices, extending previous work and deriving new mass gap results for compact groups.

Findings

Established a new measure for non-abelian connections

Developed an infinite-dimensional calculus on the lattice

Derived new results on the mass gap for compact groups

Abstract

Using projective limits as subsets of Cartesian products of homomorphisms from a lattice to the structure group, a consistent interaction measure and an infinite-dimensional calculus has been constructed for a theory of non-abelian generalized connections on a hypercubic lattice. Here, after reviewing and clarifying past work, new results are obtained for the mass gap when the structure group is compact.