arXiv:0905.3900v3 [gr-qc] 3 Aug 2010 Preprint typeset in JHEP style - HYPER VERSIONarXiv:0905.3900 Dirac quantization of membrane winding uniformly in time dependent orbifold Przemyslaw Malkiewicz†and Wlodzimierz Piechocki‡ Theoretical Physics Department Institute for Nuclear Studies Ho˙za 69, 00-681 Warszawa, Poland; E-mail:†pmalk@fuw.edu.pl,‡piech@fuw.edu.pl 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. Keywords:Spacetime Singularities, p-branes, Field Theories in Higher Dimensions.
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