Matrix regularization for tensor fields

TL;DR

This paper introduces a new matrix regularization method for tensor fields, representing them as matrices to unify transformations like area-preserving diffeomorphisms and local rotations, and relates the matrix commutator to the covariantized Poisson bracket.

Contribution

It presents a novel matrix regularization framework for tensor fields that unifies geometric transformations and connects matrix commutators with covariant Poisson brackets.

Findings

Matrix regularization describes tensor fields as matrices.

Unitary similarity transformations represent geometric symmetries.

Matrix commutator approximates covariant Poisson brackets in large-N limit.

Abstract

We propose a novel matrix regularization for tensor fields. In this regularization, tensor fields are described as rectangular matrices and both area-preserving diffeomorphisms and local rotations of the orthonormal frame are realized as unitary similarity transformations of matrices in a unified way. We also show that the matrix commutator corresponds to the covariantized Poisson bracket for tensor fields in the large-$N$ limit.