Cosmología cuántica de lazos y campos fermiónicos

Abstract

Quantum Field Theory (QFT) in curved spacetimes is subject to an inherent ambiguity that allows for an in nite freedom in the choice of vacuum, even for free eld Fock descriptions. In non-stationary backgrounds, this ambiguity cannot be eliminated, in general, by symmetry considerations. In turn, it is common that the non-stationarity of the background entails a serious obstruction to the unitary implementability of the eld dynamics. This situation poses a fundamental problem if one wants to maintain the usual probabilistic interpretation of Quantum Mechanics, and hence coherence in the quantum evolution. Fortunately, for free scalar elds in conformally ultrastatic spacetimes, such as those describing homogeneous and isotropic cosmologies, it has recently been shown that the requirement of a unitary implementation of the dynamics, together with the invariance of the quantum structures under the symmetries of the system, guarantees the uniqueness of the Fock quantization (modulo unitary transformations). It is of the greatest interest extending these uniqueness results to other elds that can describe more realistic matter content in the Universe, such as fermion els. In this thesis, we successfully address this problem for the Dirac eld, demonstrating the uniqueness of its Fock representation under our criterion of unitarity of the dynamics and invariance under the physical symmetries. We prove this uniqueness in two di erent scenarios. The rst one is a Dirac eld in three-dimensional conformally ultrastatic spacetimes, with applications in condensed matter theory...