Fock-Schwinger proper time formalism for p-branes

TL;DR

This paper extends the Fock-Schwinger proper time formalism from point particles to p-branes, embedding constrained p-brane theories into a larger, constraint-free framework with straightforward quantization and hierarchical state relationships.

Contribution

It introduces a novel formalism for p-branes using the Fock-Schwinger proper time approach, simplifying quantization and connecting different dimensional brane states.

Findings

Quantization is straightforward and elegant within the new formalism.

Conventional p-brane states are stationary solutions to a functional Schrödinger equation.

Lower-dimensional p-brane states can be viewed as special states of higher-dimensional branes.

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 p-branes which can be considered as a points in an infinite dimensional space M. The quantization appears to be straightforward and elegant. The conventional p-brane states are particular stationary solutions to the functional Schr\"odinger equation which describes the evolution of a membrane's state with respect to the invariant evolution parameter $\tau$. It is also shown that states of a lower dimensional p-brane can be considered as particular states of a higher dimensional p-brane.