A Lattice Gauge Model of Singular Marsden-Weinstein Reduction. Part I. Kinematics

TL;DR

This paper develops a lattice gauge model for SU(3) using singular symplectic reduction to construct and describe the reduced phase space, providing new insights into the kinematics of lattice gauge theories.

Contribution

It introduces a novel application of singular symplectic reduction to a classical SU(3) lattice gauge model, offering two equivalent descriptions of the reduced phase space.

Findings

Reduced phase space constructed via singular symplectic reduction

Two equivalent descriptions: symplectic covering and invariants

Provides a foundation for further dynamical analysis

Abstract

The simplest nontrivial toy model of a classical SU(3) lattice gauge theory is studied in the Hamiltonian approach. By means of singular symplectic reduction, the reduced phase space is constructed. Two equivalent descriptions of this space in terms of a symplectic covering as well as in terms of invariants are derived.