Moyal Brackets in M-Theory

TL;DR

This paper explores the use of Moyal Brackets to describe the infinite limit of Matrix Theory in 4 and 10 dimensions, providing a framework for solutions via non-local spinor bilinears that generalize Wigner functions.

Contribution

It introduces a novel approach to Matrix Theory using Moyal Brackets and constructs solutions through non-local spinor bilinears, extending phase space methods.

Findings

Established a Bogomol'nyi bound in Euclideanized equations.

Linked solutions to non-local spinor bilinear representations.

Connected Moyal Brackets with Matrix Theory in specific dimensions.

Abstract

The infinite limit of Matrix Theory in 4 and 10 dimensions is described in terms of Moyal Brackets. In those dimensions there exists a Bogomol'nyi bound to the Euclideanized version of these equations, which guarantees that solutions of the first order equations also solve the second order Matrix Theory equations. A general construction of such solutions in terms of a representation of the target space co-ordinates as non-local spinor bilinears, which are generalisations of the standard Wigner functions on phase space, is given.