Dirac quantization of membrane winding uniformly in time dependent orbifold
- 182 Downloads
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.
Keywordsp-branes Field Theories in Higher Dimensions Spacetime Singularities
- P.A.M. Dirac, Lectures on quantum mechanics, Belfer Graduate School of Science Monographs Series, New York U.S.A. (1964).Google Scholar
- A. Trautman Differential geometry for physicists, Stony Brook Lectures, (1984).Google Scholar
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.