Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

13 pags.We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.She also recognizes the hospitality provided by the High Energy Physics Department of the Radboud University Nijmegen during the months of April and May, 2016. This work was partially supported by the research grants MINECO Project No. FIS2014-54800-C2-2-P from Spain, DGAPA-UNAM IN113115 and CONACyT 237351 from Mexico, and COST Action MP1405 QSPACE supported by COST (European Cooperation in Science and Technology). In addition, M. M-B acknowledges financial support from the Netherlands Organization for Scientific Research (NWO) (Project No. 680-47-433).Peer Reviewe