A New Matrix Model for Noncommutative Field Theory

TL;DR

This paper introduces a novel matrix model regularization for noncommutative quantum field theories on the torus, utilizing Elliott-Evans decomposition and noncommutative solitons, offering new insights into field regularization methods.

Contribution

It presents a new regularization approach for noncommutative field theory using one-dimensional matrix models based on the Elliott-Evans decomposition.

Findings

Matrix trajectories derived from noncommutative solitons

Comparison with traditional zero-dimensional matrix models

Potential applications in noncommutative quantum field theory

Abstract

We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus algebra. The matrix trajectories are obtained via the expansion of fields in a basis of new noncommutative solitons described by projections and partial isometries. The matrix quantum mechanics are compared with the usual zero-dimensional matrix model regularizations and some applications are sketched.