Light-cone SU(2) Yang-Mills theory and conformal mechanics

TL;DR

This paper analyzes the light-cone SU(2) Yang-Mills theory, deriving a constrained mechanical model that reduces to conformal mechanics, revealing new constraints and classical equivalence to free particle dynamics.

Contribution

It introduces a detailed Hamiltonian analysis of light-cone SU(2) Yang-Mills mechanics, uncovering additional constraints and linking it to conformal mechanics.

Findings

Classical evolution matches free one-dimensional particle dynamics.

The model includes new first and second class constraints.

Complex solutions relate to inverse square interaction in conformal mechanics.

Abstract

We examine the mechanical matrix model that can be derived from the SU(2) Yang-Mills light-cone field theory by restricting the gauge fields to depend on the light-cone time alone. We use Dirac's generalized Hamiltonian approach. In contrast to its well-known instant-time counterpart the light-cone version of SU(2) Yang-Mills mechanics has in addition to the constraints, generating the SU(2) gauge transformations, the new first and second class constraints also. On account of all of these constraints a complete reduction in number of the degrees of freedom is performed. It is argued that the classical evolution of the unconstrained degrees of freedom is equivalent to a free one-dimensional particle dynamics. Considering the complex solutions to the second class constraints we show at this time that the unconstrained Hamiltonian system represents the well-known model of conformal mechanics with a ``strength'' of the inverse square interaction determined by the value of the gauge field spin.