Dirac quantization of membrane winding uniformly in time dependent orbifold

  • Przemys law Małkiewicz
  • W lodzimierz Piechocki
Open Access


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.


p-branes Field Theories in Higher Dimensions Spacetime Singularities 


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© The Author(s) 2010

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.

Authors and Affiliations

  • Przemys law Małkiewicz
    • 1
  • W lodzimierz Piechocki
    • 1
  1. 1.Theoretical Physics DepartmentInstitute for Nuclear StudiesWarszawaPoland

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