The Classical and Quantum Theory of Relativistic p-Branes without Constraints

TL;DR

This paper develops a relativistic p-brane theory that does not require reparametrization constraints, allowing straightforward quantization and introducing elastic deformation degrees of freedom, which include solutions of traditional models.

Contribution

It introduces a novel unconstrained relativistic p-brane theory that simplifies quantization and incorporates elastic deformation degrees of freedom.

Findings

No reparametrization constraints are necessary in the new theory.

The theory includes additional physical degrees of freedom related to membrane elasticity.

Conventional p-brane solutions are recovered within the new framework.

Abstract

It is shown that a relativistic (i.e. a Poincar{\' e} invariant) theory of extended objects (called p-branes) is not necessarily invariant under reparametrizations of corresponding $p$-dimensional worldsheets (including worldlines for $p = 0$). Consequnetly, no constraints among the dynamical variables are necessary and quantization is straightforward. Additional degrees of freedom so obtained are given a physical interpretation as being related to membrane's elastic deformations ("wiggleness"). In particular, such a more general, unconstrained theory implies as solutions also those p-brane states that are solutions of the conventional theory of the Dirac-Nambu-Goto type.