Nonabelian lattice theories: Consistent measures and strata

TL;DR

This paper investigates the conditions for consistent measures in nonabelian lattice theories, exploring their impact on the Hamiltonian potential and the existence of a mass gap.

Contribution

It provides general conditions for measures to ensure consistency, positivity, and a mass gap in nonabelian lattice theories, and discusses the influence of nongeneric strata.

Findings

Derived conditions for measure consistency and positivity

Analyzed the impact of nongeneric strata on the Hamiltonian potential

Discussed implications for the mass gap in nonabelian lattice theories

Abstract

The role of consistent measures in the rigorous construction of nonabelian lattice theories is analized. General conditions that measures must fulfill to insure consistency, positivity and a mass gap are obtained. The impact of nongeneric strata on the nature of the Hamiltonian lattice potential is also discussed.