Planar Yang-Mills theory: Hamiltonian, regulators and mass gap

TL;DR

This paper analyzes the Hamiltonian formulation of (2+1)-dimensional non-Abelian Yang-Mills theory, focusing on regularization, the mass gap, and explicit eigenstates, providing insights into the theory's spectral properties.

Contribution

It introduces a gauge-invariant matrix parametrization, discusses regularization and renormalization, and explicitly constructs the lowest eigenstates demonstrating the mass gap in the theory.

Findings

Explicit lowest eigenstates with zero charge are obtained.

The mass gap is identified and analyzed.

Regularization and renormalization procedures are detailed.

Abstract

We carry out the Hamiltonian analysis of non-Abelian gauge theories in (2+1) dimensions in a gauge-invariant matrix parametrization of the fields. A detailed discussion of regularization issues and the construction of the renormalized Laplace operator on the configuration space, which is proportional to the kinetic energy, are given. The origin of the mass gap is analyzed and the lowest eigenstates of the kinetic energy are explicitly obtained; these have zero charge and exhibit a mass gap . The nature of the corrections due to the potential energy, the possibility of an improved perturbation theory and a Schrodinger-like equation for the states are also discussed.