On Unitary Time Evolution in Gowdy $T^3$ Cosmologies

Details On Unitary Time Evolution in Gowdy $T^3$ Cosmologies On Unitary Time Evolution in Gowdy $T^3$ Cosmologies

2002-04-16

arxiv.org/abs/gr-qc/0204053v2

Int.J.Mod.Phys. D11 (2002) 1451-1468

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, no figures, latex file; references added, a proof included. Final version to appear in IJMPD

Scientific paper

A non-perturbative canonical quantization of Gowdy $T^3$ polarized models carried out recently is considered. This approach profits from the equivalence between the symmetry reduced model and 2+1 gravity coupled to a massless real scalar field. The system is partially gauge fixed and a choice of internal time is performed, for which the true degrees of freedom of the model reduce to a massless free scalar field propagating on a 2-dimensional expanding torus. It is shown that the symplectic transformation that determines the classical dynamics cannot be unitarily implemented on the corresponding Hilbert space of quantum states. The implications of this result for both quantization of fields on curved manifolds and physically relevant questions regarding the initial singularity are discussed.

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