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Quantum Gowdy T3 model: A unitary description

Alejandro Corichi1,2,*, Jerónimo Cortez3,†, and Guillermo A. Mena Marugán3,‡

  • 1Instituto de Matemáticas, Universidad Nacional Autónoma de México A. Postal 61-3, Morelia, Michoacán 58090, Mexico
  • 2Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México A. Postal 70-543, México D.F. 04510, Mexico
  • 3Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain

  • *Electronic address: corichi@matmor.unam.mx
  • †Electronic address: jacq@iem.cfmac.csic.es
  • ‡Electronic address: mena@iem.cfmac.csic.es
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Phys. Rev. D 73, 084020 – Published 19 April, 2006

DOI: https://doi.org/10.1103/PhysRevD.73.084020

Abstract

The quantization of the family of linearly polarized Gowdy T3 spacetimes is discussed in detail, starting with a canonical analysis in which the true degrees of freedom are described by a scalar field that satisfies a Klein-Gordon type equation in a fiducial time-dependent background. A time-dependent canonical transformation, which amounts to a change of the basic (scalar) field of the model, brings the system to a description in terms of a Klein-Gordon equation on a background that is now static, although subject to a time-dependent potential. The system is quantized by means of a natural choice of annihilation and creation operators. The quantum time evolution is considered and shown to be unitary, so that both the Schrödinger and Heisenberg pictures can be consistently constructed. This has to be contrasted with previous treatments for which time evolution failed to be implementable as a unitary transformation. Possible implications for both canonical quantum gravity and quantum field theory in curved spacetime are noted.

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Phys. Rev. D 73, 084020– Published 19 April, 2006
  • Received 3 March 2006

© 2006 American Physical Society

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