Dirac quantization of membrane winding uniformly in time dependent orbifold
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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
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