Schrodinger representation for the polarized Gowdy model

Details Schrodinger representation for the polarized Gowdy model Schrodinger representation for the polarized Gowdy model

2006-07-20

arxiv.org/abs/gr-qc/0607084v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages

Scientific paper

10.1088/0264-9381/24/1/001

The polarized ${\bf T}^3$ Gowdy model is, in a standard gauge, characterized by a point particle degree of freedom and a scalar field degree of freedom obeying a linear field equation on ${\bf R}\times{\bf S}^1$. The Fock representation of the scalar field has been well-studied. Here we construct the Schrodinger representation for the scalar field at a fixed value of the Gowdy time in terms of square-integrable functions on a space of distributional fields with a Gaussian probability measure. We show that ``typical'' field configurations are slightly more singular than square-integrable functions on the circle. For each time the corresponding Schrodinger representation is unitarily equivalent to the Fock representation, and hence all the Schrodinger representations are equivalent. However, the failure of unitary implementability of time evolution in this model manifests itself in the mutual singularity of the Gaussian measures at different times.

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