The canonical quantization of the minisuperspace model describing cylindrically symmetric gravitational waves with two polarizations is presented. A Fock space-type representation is constructed. It is based on a complete set of quantum observables. Physical expectation values may be calculated in arbitrary excitations of the vacuum. Our approach provides a nonlinear generalization of the quantization of the collinearly polarized Einstein-Rosen gravitational waves.
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Korotkin et al. (1998) studied this question.
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