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On time evolution in quantum Gowdy \(T^3\) models. (English) Zbl 1326.83038
Summary: The canonical (non-perturbative) quantization of Gowdy \(T^3\) polarized models carried out recently by M. Pierri [Int. J. Mod. Phys. D 11, No. 1, 135–153 (2002; Zbl 1062.83037); “Hamiltonian and volume operators”, preprint, arXiv:gr-qc/0201013] is analyzed. The model is based on the analogy with 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.
83C45 Quantization of the gravitational field
81S99 General quantum mechanics and problems of quantization