The pseudoparticle approach for solving path integrals in gauge theories

TL;DR

This paper introduces a pseudoparticle method for numerically evaluating path integrals in gauge theories, successfully reproducing known potentials and demonstrating confinement in SU(2) Yang-Mills theory.

Contribution

The paper presents a novel pseudoparticle approach for solving path integrals in gauge theories, offering a new computational technique with results consistent with established lattice calculations.

Findings

Accurately reproduces Coulomb potential in Maxwell theory.

Provides evidence of confinement in SU(2) Yang-Mills theory.

Shows consistent scaling of physical quantities with coupling constant.

Abstract

We present a numerical technique for calculating path integrals in non-compact U(1) and SU(2) gauge theories. The gauge fields are represented by a superposition of pseudoparticles of various types with their amplitudes and color orientations as degrees of freedom. Applied to Maxwell theory this technique results in a potential which is in excellent agreement with the Coulomb potential. For SU(2) Yang-Mills theory the same technique yields clear evidence of confinement. Varying the coupling constant exhibits the same scaling behavior for the string tension, the topological susceptibility and the critical temperature while their dimensionless ratios are similar to those obtained in lattice calculations.