Three Dimensional Simplicial Yang-Mills Theory: An Approach to the Mass Gap

TL;DR

This paper formulates 2+1 dimensional Yang-Mills theory using a simplicial regularization approach, constructs its quantization, and explores the implications for the mass gap and continuum limit.

Contribution

It introduces a novel simplicial Hamiltonian formulation of 2+1D Yang-Mills theory with a focus on mass gap analysis and continuum limit construction.

Findings

Hamiltonian formulation within simplicial regularization

Approximate conformal invariance aids continuum limit

Insights into the mass gap in 2+1D Yang-Mills theory

Abstract

We show how to formulate Yang-Mills Theory in \m{2+1} dimensions as a hamitonian system within a simplicial regularization and construct its quantization, with special attention to the mass gap. An approximate conformal invariance of the hamiltonian of this theory is useful to construct a continuum limit.