We study several issues related to the different choices of time available for the classical and quantum treatment of linearly polarized cylindrical gravitational waves. We pay special attention to the time evolution of creation and annihilation operators and the definition of Fock spaces for the different choices of time involved. We also discuss the issue of microcausality and the use of field commutators to extract information about the causal properties of quantum spacetime.
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G. et al. (2003) studied this question.
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