M-theory and Deformation Quantization

TL;DR

This paper explores the application of Zariski deformation quantization to the Nambu brackets in p-brane actions, proposing a covariant formulation of Matrix theory within M-theory.

Contribution

It introduces the use of Zariski deformation quantization for Nambu brackets and applies it to develop a covariant Matrix theory formulation in M-theory.

Findings

Zariski deformation quantization can be applied to Nambu brackets.

A covariant formulation of Matrix theory is proposed using this quantization.

The approach offers a new perspective on quantizing p-brane actions.

Abstract

We discuss deformation quantization of the covariant, light-cone and conformal gauge-fixed p-brane actions (p>1) which are closely related to the structure of the classical and quantum Nambu brackets. It is known that deformation quantization of the Nambu bracket is not of the usual Moyal type. Yet the Nambu bracket can be quantized using the Zariski deformation quantization (discovered by Dito, Flato, Sternheimer and Takhtajan) which is based on factorization of polynomials in several real variables. We discuss a particular application of the Zariski deformed quantization in M-theory by considering the problem of a covariant formulation of Matrix theory. We propose that the problem of a covariant formulation of Matrix theory can be solved using the formalism of Zariski deformed quantization of the triple Nambu bracket.