Dirac quantization of membrane in time dependent orbifold

TL;DR

This paper develops a quantum theory for membranes near time-dependent orbifold singularities, showing that their dynamics are equivalent to closed strings in FRW spacetime, and constructs the physical Hilbert space with non-trivial states crossing the singularity.

Contribution

It introduces a novel quantum framework for membranes in time-dependent orbifolds, extending string quantization methods to higher-dimensional objects and singular spacetimes.

Findings

Existence of non-trivial quantum states crossing the singularity

Membrane dynamics equivalent to closed strings in FRW spacetime

Construction of the membrane's physical Hilbert space

Abstract

We present quantum theory of a membrane propagating in the vicinity of a time dependent orbifold singularity. The dynamics of a membrane, with the parameters space topology of a torus, winding uniformly around compact dimension of the embedding spacetime is mathematically equivalent to the dynamics of a closed string in a flat FRW spacetime. The construction of the physical Hilbert space of a membrane makes use of the kernel space of self-adjoint constraint operators. It is a subspace of the representation space of the constraints algebra. There exist non-trivial quantum states of a membrane evolving across the singularity.