Ponente
Descripción
I study the Fock representations for a Dirac field given by the the different choices of creation and annihilation variables. This is done in the context of a perturbed flat cosmology that, in addition, is minimally coupled to fermionic perturbations. In our description, I use a canonical formulation for the entire system, formed by the underlying cosmological spacetime and all its perturbations. I start with the family of vacua that allows a unitarily implementable quantum evolution that is employed in hybrid quantum cosmology. Then, its restriction to that lead to some finite ultraviolet backreaction in the quantum Hamiltonian constraint and to a fermionic Hamiltonian operator that is properly defined in the span of the n-particle/antiparticle states, in the context of hybrid quantum cosmology. The ultimate step comes with a completely diagonal quan- tum evolution, achieved by restricting our choice to an almost complete extent. I compare these results with the ones given by the so-called adiabatic scheme which was originally developed in the context of quantum field theory in fixed cosmological backgrounds, I find that all adiabatic states belong to the unitary equivalence class of Fock representations that allow a unitarily implementable quantum evolution. In particular, this unitarity of the dynamics ensures that the vacua defined with adiabatic initial conditions at different times are unitar- ily equivalent. Finally, all adiabatic orders other than zero allow the definition of annihilation and creation operators for the Dirac field with appropriate ultraviolet properties.
