Schrodinger representation for the polarized Gowdy model

Abstract

The polarized ${\mathbf{T}}^3$ 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 $\mathbf{R}\times {\mathbf{S}}^1$. 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.

13 pages

Cited by in corpus (7)

• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics
• The time-dependent quantum harmonic oscillator revisited: Applications to Quantum Field Theory
• Quantum unitary evolution of linearly polarized S^1\times S^2 and S^3 Gowdy models coupled to massless scalar fields
• Loop Quantization of Polarized Gowdy Model on $T^3$: Kinematical States and Constraint Operators
• Loop Quantization of Polarized Gowdy Model on $T^3$: Classical Theory
• Hamiltonian Dynamics of Linearly Polarized Gowdy Models Coupled to Massless Scalar Fields
• Schrodinger quantization of linearly polarized Gowdy $S^1\times S^2$ and $S^3$ models coupled to massless scalar fields