Covariant quantization of membrane dynamics

Lee Smolin
Phys. Rev. D 57, 6216 – Published 15 May 1998
PDFExport Citation

Abstract

A Lorentz covariant quantization of membrane dynamics is defined, which also leaves unbroken the full three dimensional diffeomorphism invariance of the membrane. This makes it possible to understand the reductions to string theory directly in terms of the Poisson brackets and constraints of the theories. Two approaches to the covariant quantization are studied, Dirac quantization and a quantization based on matrices, which play a role in recent work on M theory. In both approaches the dynamics is generated by a Hamiltonian constraint, which means that all physical states are “zero energy.” A covariant matrix formulation may be defined, but it is not known if the full diffeomorphism invariance of the membrane may be consistently imposed. The problem is the non-area-preserving diffeomorphisms: they are realized nonlinearly in the classical theory, but 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.

  • Received 3 November 1997

DOI:https://doi.org/10.1103/PhysRevD.57.6216

©1998 American Physical Society

Authors & Affiliations

Lee Smolin*

  • Center for Gravitational Physics and Geometry, Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802

  • *Email address: smolin@phys.psu.edu

References (Subscription Required)

Click to Expand
Issue

Vol. 57, Iss. 10 — 15 May 1998

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×