Covariant quantization of membrane dynamics

TL;DR

This paper develops a Lorentz covariant quantization method for membrane dynamics that preserves full diffeomorphism invariance, explores reductions to string theory, and discusses challenges in matrix regularization and background independence.

Contribution

It introduces a covariant quantization framework for membranes, extending beyond light-cone gauge, and addresses gauge symmetry implementation issues in matrix regularization.

Findings

Covariant quantization preserves full diffeomorphism invariance.

Difficulties in implementing non-area-preserving diffeomorphisms at finite N.

Proposed approach for background independent matrix dynamics.

Abstract

A Lorentz covariant quantization of membrane dynamics is defined, which also leaves unbroken the full three dimensional diffeomorphism invariance of the membrane. Among the applications studied are the reduction to string theory, which may be understood in terms of the phase space and constraints, and the interpretation of physical,zero-energy states. A matrix regularization is defined as in the light cone gauged fixed theory but there are difficulties implementing all the gauge symmetries. The problem involves the non-area-preserving diffeomorphisms which are realized non-linearly in the classical theory. In the quantum theory they do not seem to have a consistent implementation for finite N. Finally, an approach to a genuinely background independent formulation of matrix dynamics is briefly described.