Function group approach to unconstrained Hamiltonian Yang-Mills theory

TL;DR

This paper develops a canonical transformation approach to reformulate the classical SU(2) Yang-Mills Hamiltonian, resulting in a local, unconstrained Hamiltonian expressed as a finite Laurent series in the coupling constant.

Contribution

It introduces a novel function group approach that parametrizes Gauss law generators and derives a local unconstrained Hamiltonian for Yang-Mills theory.

Findings

The unconstrained Hamiltonian is local and expressed as a finite Laurent series.

The method provides a systematic way to handle gauge constraints in Yang-Mills theory.

The approach simplifies the Hamiltonian structure for classical SU(2) Yang-Mills.

Abstract

Starting from the temporal gauge Hamiltonian for classical pure Yang-Mills theory with the gauge group SU(2) a canonical transformation is initiated by parametrising the Gauss law generators with three new canonical variables. The construction of the remaining variables of the new set proceeds through a number of intermediate variables in several steps, which are suggested by the Poisson bracket relations and the gauge transformation properties of these variables. The unconstrained Hamiltonian is obtained from the original one by expressing it in the new variables and then setting the Gauss law generators to zero. This Hamiltonian turns out to be local and it decomposes into a finite Laurent series in powers of the coupling constant.