A consistent measure for lattice Yang-Mills

TL;DR

This paper develops a mathematically rigorous, consistent measure for lattice Yang-Mills theory, enabling better non-perturbative analysis of quantum chromodynamics (QCD), and presents new results on the mass gap for compact structure groups.

Contribution

It constructs a new, consistent measure for lattice Yang-Mills theory using projective limits, advancing the mathematical foundation for non-perturbative QCD studies.

Findings

Constructed a consistent interaction measure for non-abelian generalized connections.

Developed an infinite-dimensional calculus on the lattice measure.

Derived new results concerning the mass gap for compact structure groups.

Abstract

The construction of a consistent measure for Yang-Mills is a precondition for an accurate formulation of non-perturbative approaches to QCD, both analytical and numerical. 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.