Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory

TL;DR

This paper develops a matrix approximation framework for noncommutative field theories on a torus, applying it to scalar, tachyon, and gauge theories, and analyzing soliton dynamics and classifications.

Contribution

It introduces a matrix algebra approach to approximate noncommutative torus field theories, enabling analysis of soliton dynamics and their classifications.

Findings

Matrix algebra approximates noncommutative torus functions.

Applied to scalar, tachyon, and gauge theories.

Compared soliton dynamics on torus and plane.

Abstract

We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is applied to the perturbative dynamics of scalar field theory, to tachyon dynamics in string field theory, and to the Hamiltonian dynamics of noncommutative gauge theory in two dimensions. We also describe the adiabatic dynamics of solitons on the noncommutative torus and compare various classes of noncommutative solitons on the torus and the plane.