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Author: Álvaro Torres-Caballeros Instituto de Estructura de la Materia, IEM-CSIC Serrano 121, 28006 Madrid, Spain alvaro.torres@iem.cfmac.csic.es Co-authors: Jerónimo Cortez Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México. Ciudad de México 04510, Mexico jacq@ciencias.unam.mx Beatriz Elizaga Navascués Department of Physics and Astronomy, Louisiana State University Baton Rouge, LA 70803-4001, USA bnavascues@lsu.edu Guillermo A. Mena Marugán Instituto de Estructura de la Materia, IEM-CSIC Serrano 121, 28006 Madrid, Spain mena@iem.cfmac.csic.es José Velhinho Faculdade de Ciências and FibEnTech-UBI, Universidade da Beira Interior R. Marquês D’Ávila e Bolama, 6201-001 Covilhã, Portugal jvelhi@ubi.pt ABSTRACT: We discuss a criterion to guarantee the uniqueness of the Fock quantization of a massless free scalar field in a Kantowski-Sachs background. In general spacetimes, the infinite ambiguity of choosing a set of annihilation and creation operators leads to non-equivalent Fock representations, a fact that is due to the unavailability of a privileged vacuum state in the theory. In the case of a Kantowski-Sachs spacetime, we show that the problem can be overcome by imposing invariance under the spatial symmetries of the background and quantum dynamics that admit a unitary implementation. We also show that this criterion fixes the freedom for background-dependent scalings involved in the choice of creation and annihilation variables. The remaining freedom for background-dependent changes can be employed to attain a Hamiltonian for the scalar field that is asymptotically diagonal in the ultraviolet sector. These results may find applications in the quantization of matter fields and perturbations on anisotropic cosmologies and, moreover, on the interior of nonrotating black hole spacetimes.
