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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.
##### MSC:
 83C45 Quantization of the gravitational field 81S99 General quantum mechanics and problems of quantization