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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/076/03/0407-0420

    • Keywords

       

      Quantum mechanics in curved space; non-linear sigma model; Virasoro algebra.

    • Abstract

       

      We study a particular approach for analysing worldsheet conformal invariance for bosonic string propagating in a curved background using Hamiltonian formalism. We work in the Schrödinger picture of a single-particle description of the problem where the particle moves in an infinite-dimensional space. Background independence is maintained in this approach by adopting DeWitt’s (Phys. Rev. 85, 653–661, 1952) coordinate-independent formulation of quantum mechanics. This enables us to construct certain background-independent notion of Virasoro generators, called DeWitt–Virasoro (DWV) generators, and invariant matrix elements of an arbitrary operator constructed out of them in spin-zero representation. We show that the DWV algebra is given by the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. The actual quantum Virasoro generators should be obtained by first introducing the vacuum state and then normal ordering the DWV generators with respect to that. We demonstrate the procedure in flat and pp-wave backgrounds.

    • Author Affiliations

       

      Partha Mukhopadhyay1

      1. The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600 113, India
    • Dates

       
  • Pramana – Journal of Physics | News

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