Polymer parametrized field theory

Alok Laddha and Madhavan Varadarajan
Phys. Rev. D 78, 044008 – Published 18 August 2008

Abstract

Free scalar field theory on 2-dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using loop quantum gravity (LQG) type “polymer” representations for the matter field and the inertial variables. The quantum constraints are solved via group averaging techniques and, analogous to the case of spatial geometry in LQG, the smooth (flat) spacetime geometry is replaced by a discrete quantum structure. An overcomplete set of Dirac observables, consisting of (a) (exponentials of) the standard free scalar field creation-annihilation modes and (b) canonical transformations corresponding to conformal isometries, are represented as operators on the physical Hilbert space. None of these constructions suffer from any of the “triangulation”-dependent choices which arise in treatments of LQG. In contrast to the standard Fock quantization, the non-Fock nature of the representation ensures that the group of conformal isometries as well as that of the gauge transformations generated by the constraints are represented in an anomaly free manner. Semiclassical states can be analyzed at the gauge invariant level. It is shown that “physical weaves” necessarily underlie such states and that such states display semiclassicality with respect to, at most, a countable subset of the (uncountably large) set of observables of type (a). The model thus offers a fertile testing ground for proposed definitions of quantum dynamics as well as semiclassical states in LQG.

  • Received 25 May 2008

DOI:https://doi.org/10.1103/PhysRevD.78.044008

©2008 American Physical Society

Authors & Affiliations

Alok Laddha

  • The Institute of Mathematical Sciences, Chennai-600 113, India

Madhavan Varadarajan

  • Raman Research Institute, Bangalore-560 080, India

  • *alokl@imsc.res.in
  • madhavan@rri.res.in

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Vol. 78, Iss. 4 — 15 August 2008

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