Jerónimo Cortez, Guillermo A. Mena Marugán, Javier Olmedo, José M. Velhinho
The quantization of scalar fields in nonstationary spacetimes is plagued with ambiguities that undermine the significance of physical predictions. A context in which this kind of ambiguities arises and prevents the derivation of robust results is, e.g., in the quantum analysis of cosmological perturbations. In these situations, typically, a suitable scaling of the field by a time dependent function leads to a description in an auxiliary static background, though the nonstationarity still shows up in a time dependent mass. For such a field description, and assuming the compactness of the spatial sections, we recently proved in three or less spatial dimensions that the criteria of a natural implementation of the spatial isometries and of a unitary time evolution are able to select a unique class of unitarily equivalent vacua, and hence of Fock representations. In this work, we extend our uniqueness result to the consideration of all possible field descriptions that can be reached by a time dependent canonical transformation which, in particular, involves a scaling of the field by a function of time. This kind of canonical transformations modify the dynamics of the system. Remarkably, for {\emph {any}} compact spatial manifold in less than four dimensions, we show that our criteria eliminate any possible nontrivial scaling of the field other than that leading to the description in an auxiliary static background. Besides, we show that either no time dependent redefinition of the field momentum is allowed or, if this may happen, the redefinition does not introduce any Fock representation that cannot be obtained by a unitary transformation. In total, our results imply the uniqueness of the Fock quantization, including both the choice of field description and of a Fock representation for it.
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http://arxiv.org/abs/1202.6330
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