UNIQUENESS OF THE QUANTIZATION OF A SCALAR FIELD ON S1 WITH TIME DEPENDENT MASS: A GENERALIZATION OF THE CASE OF GOWDY COSMOLOGIES
The canonical quantization of midisuperspace gravitational models is a particular case of the quantization of fields. Typically, the requirement of symmetries other than homogeneity reduces the phase space of full General Relativity, but still leaves an infinite number of degrees of freedom, encoded in some fields which parametrize the metric components and are subject to constraints. Since the total Hamiltonian vanishes, and constraints are all that there is left, a peculiar situation occurs in the quantization of these models. On the one hand, it is tempting to solve at the classical level as many constraints as possible, e.g. by gauge fixing or other means. On the other hand, if all the constraints were to be solved, one would be left just with the infinite dimensional reduced phase space of the model, and no extra structure to guide us through the quantization process.
