Quantum Gowdy T3 model: Schrödinger representation with unitary dynamics

Alejandro Corichi, Jerónimo Cortez, Guillermo A. Mena Marugán, and José M. Velhinho
Phys. Rev. D 76, 124031 – Published 27 December 2007

Abstract

The linearly polarized Gowdy T3 model is paradigmatic for studying technical and conceptual issues in the quest for a quantum theory of gravity since, after a suitable and almost complete gauge fixing, it becomes an exactly soluble midisuperspace model. Recently, a new quantization of the model, possessing desired features such as a unitary implementation of the gauge group and of the time evolution, has been put forward and proven to be essentially unique. An appropriate setting for making contact with other approaches to canonical quantum gravity is provided by the Schrödinger representation, where states are functionals on the configuration space of the theory. Here we construct this functional description, analyze the time evolution in this context and show that it is also unitary when restricted to physical states, i.e. states which are solutions to the remaining constraint of the theory.

  • Received 1 October 2007

DOI:https://doi.org/10.1103/PhysRevD.76.124031

©2007 American Physical Society

Authors & Affiliations

Alejandro Corichi1,2,*, Jerónimo Cortez3,†, Guillermo A. Mena Marugán4,‡, and José M. Velhinho5,§

  • 1Instituto de Matemáticas, Universidad Nacional Autónoma de México, UNAM-Campus Morelia, Apartado Postal 61-3, Morelia, Michoacán 58090, Mexico
  • 2Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, Pennsylvania 16802, USA
  • 3Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Apartado Postal 50-542, México D.F. 04510, Mexico
  • 4Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain
  • 5Departamento de Física, Universidade da Beira Interior, Rua Marquês D’Ávila e Bolama, 6201-001 Covilhã, Portugal

  • *corichi@matmor.unam.mx
  • jacq@fciencias.unam.mx
  • mena@iem.cfmac.csic.es
  • §jvelhi@ubi.pt

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Issue

Vol. 76, Iss. 12 — 15 December 2007

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