The Dirac-Nambu-Goto p-Branes as Particular Solutions to a Generalized, Unconstrained Theory

TL;DR

This paper extends the theory of p-branes into an unconstrained, covariant framework using an infinite-dimensional membrane space, providing new solutions and a straightforward quantization approach.

Contribution

It introduces a generalized unconstrained p-brane theory with a covariant action in membrane space, including new solutions and a clear quantization method.

Findings

Conventional p-brane states are stationary solutions of the functional Schrödinger equation.

A tau-dependent wave packet solution for a null p-brane is derived.

Lower-dimensional membrane states are shown to be particular cases of higher-dimensional membranes.

Abstract

The theory of the usual, constrained p-branes is embedded into a larger theory in which there is no constraints. In the latter theory the Fock-Schwinger proper time formalism is extended from point-particles to membranes of arbitrary dimension. For this purpose the tensor calculus in the infinite dimensional membrane space M is developed and an action which is covariant under reparametrizations in M is proposed. The canonical and Hamiltonian formalism is elaborated in detail. The quantization appears to be straightforward and elegant. No problem with unitarity arises. The conventional p-brane states are particular stationary solutions to the functional Schroedinger equation which describes the evolution of a membrane's state with respect to the invariant evolution parameter tau. A tau-dependent solution which corresponds to the wave packet of a null p-brane is found. It is also shown that states of a lower dimensional membrane can be considered as particular states of a higher dimensional membrane.