Covariant quantization of membrane 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.

Latex, 21 pages, no figures

References in corpus (3)

• Dual formulation of spin network evolution
• A note on the gauge symmetries of pure Chern-Simons theories with p-form gauge fields
• Chern-Simons theory in 11 dimensions as a non-perturbative phase of M theory

Cited by in corpus (13)

• M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
• Strings, loops and others: a critical survey of the present approaches to quantum gravity
• Orthogonal basis for the energy eigenfunctions of the Chern-Simons matrix model
• Hamiltonian dynamics of extended objects
• Membrane and Noncommutativity
• Comments on the Problem of a Covariant Formulation of Matrix Theory
• Interference and Oscillation in Nambu Quantum Mechanics
• Dirac equation for membranes
• Pointlike structure for super p-branes
• On the distance observable in the Moyal plane and in a novel two-dimensional space with string-theory pregeometry
• Hidden Symmetries of M Theory
• Dirac equation for embedded 4-geometries
• Aspects of noncommutativity in field theory, strings and membranes