Fermions in quantum cosmology

Journal Article · Sun Feb 15 04:00:00 EST 1987 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.35.1100· OSTI ID:6926023

D'Eath, P D; Halliwell, J J

This paper considers the extension of the ideas of quantum cosmology and, in particular, the proposal of Hartle and Hawking for the boundary conditions of the Universe, to models which incorporate fermions in a realistic manner. We consider inhomogeneous fermionic perturbations about a homogeneous, isotropic minisuperspace background model, by expanding the fermion fields in spinor harmonics on the spatial sections, taken to be three-spheres. The Dirac action is thus found to take the form of an infinite sum of terms, each describing a time-dependent Fermi oscillator. On quantization, we find that the Wheeler-DeWitt equation for the wave function of the Universe may be decomposed into a set of time-dependent Schroumldinger equations, one for each fermion mode, and a background minisuperspace Wheeler-DeWitt equation, which includes a term in its potential describing the back reaction of the fermionic perturbations on the homogeneous modes. Our quantization procedure employs the holomorphic representation for the fermion modes, which permits them to be treated in a manner very similar to the case of bosonic perturbations considered by Halliwell and Hawking. We set initial conditions for the Schroedinger equations by applying the proposal of Hartle and Hawking that the quantum state of the Universe is defined by a path integral over compact four-metrics and regular matter fields. We find this to imply that the fermion modes start out in their ground state. Particles are created in the subsequent (inflationary) evolution, and their number, defined with respect to instantaneous Hamiltonian diagonalization, is calculated and is found to be finite. We calculate the back-reaction term and find, after regularization, that its effect is negligible.

• Research Organization: Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, United Kingdom
• OSTI ID: 6926023
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 35:4; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

640106* -- Astrophysics & Cosmology-- Cosmology
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
COSMOLOGICAL MODELS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
FERMIONS
FUNCTIONS
GRAVITATIONAL FIELDS
HAMILTONIANS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
QUANTIZATION
QUANTUM OPERATORS
SCALAR FIELDS
SCHROEDINGER EQUATION
SPINORS
TENSOR FORCES
TIME DEPENDENCE
UNIVERSE
WAVE EQUATIONS
WAVE FUNCTIONS