Asymptotic diagonalization of the fermionic Hamiltonian in hybrid loop quantum cosmology

Abstract

We use the freedom available in hybrid loop quantum cosmology to split the degrees of freedom between the geometry and the matter fields so as to build a quantum field theory for the matter content with good quantum properties. We investigate this issue in an inflationary, flat cosmology with inhomogeneous perturbations, and focus the discussion on a Dirac field, minimally coupled to the cosmological background and treated as a perturbation. After truncating the action at the lowest nontrivial order in perturbations, one must define canonical variables for the matter content, for which one generally employs canonical transformations that mix the homogeneous background and the perturbations. Each of these possible definitions comes associated with a different matter contribution to the Hamiltonian of the complete system, that may, in general, contain terms that are quadratic in creationlike variables, and in annihilationlike variables, with the subsequent production and destruction of pairs of fermionic particles and antiparticles. We determine a choice of the fermionic canonical variables for which the interaction part of the Hamiltonian can be made as negligible as desired in the asymptotic regime of large particle/antiparticle wave numbers. Finally, we study the quantum dynamics for this choice, imposing the total Hamiltonian constraint on the quantum states and assuming that their gravitational part is not affected significantly by the presence of fermions. In this way, we obtain a Schrödinger equation for the fermionic degrees of freedom in terms of quantum expectation values of the geometry that leads to asymptotically diagonal Heisenberg relations and Bogoliubov evolution transformations, with no divergences in the associated normal-ordered Hamiltonian.

arXiv comment12 pages, matches published version

References in corpus (23)

• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Quantum Gravity and Regge Calculus
• Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
• Hybrid quantization of an inflationary universe
• Gauge-Invariant Perturbations in Hybrid Quantum Cosmology
• Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology
• Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
• The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson-Walker Spacetimes
• Hybrid Quantum Cosmology: Combining Loop and Fock Quantizations
• Uniqueness of the Fock quantization of the Gowdy $T^3$ model
• Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes
• Unique Fock quantization of scalar cosmological perturbations
• Primordial tensor modes of the early Universe
• Fock quantization of a scalar field with time dependent mass on the three-sphere: unitarity and uniqueness
• Massless scalar field in de Sitter spacetime: unitary quantum time evolution
• Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
• Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics
• Fermions in Hybrid Loop Quantum Cosmology
• Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology
• Backreaction of fermionic perturbations in the Hamiltonian of hybrid loop quantum cosmology
• Unitary evolution and uniqueness of the Fock representation of Dirac fields in cosmological spacetimes

Cited by in corpus (5)

• Hybrid Loop Quantum Cosmology: An Overview
• Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology
• Fock quantization of the Dirac field in hybrid quantum cosmology: Relation with adiabatic states
• Unique fermionic vacuum in de Sitter spacetime from hybrid quantum cosmology
• Quantum unitary dynamics of a charged fermionic field and Schwinger effect