Generalized Hamiltonian Dynamics of Friedmann Cosmology with Scalar and Spinor Matter Source Fields

TL;DR

This paper explores the classical and quantum dynamics of Friedmann cosmology with scalar and spinor matter fields using the Dirac Hamiltonian formalism, identifying conserved quantities and comparing quantization methods.

Contribution

It provides a Hamiltonian reduction for cosmological models with scalar and fermion fields, establishing a time-independent Hamiltonian and analyzing quantization approaches.

Findings

Existence of a time-independent Hamiltonian for all curvature values.

Conformal time-like Killing vectors relate to conserved energy.

Quantum observables align with classical theory expectations.

Abstract

The classical and quantum dynamics of the Friedmann-Robertson-Walker Universe with massless scalar and massive fermion matter field as a source is discussed in the framework of the Dirac generalized Hamiltonian formalism. The Hamiltonian reduction of this constrained system is realized for two cases of minimal and conformal coupling between gravity and matter. It is shown that in both cases for all values of curvature, of maximally symmetric space there exists a time independent reduced local Hamiltonian which describes the dynamics of the cosmic scale factor. The relevance of conformal time-like Killing vector fields in FRW space-time to the existence of time independent Hamiltonian and the corresponding notion of conserved energy is discussed. The extended quantization with the Wheeler-deWitt equation is compared with the canonical quantization of unconstrained system. It is shown that quantum observables treated as expectation values of the Dirac observables properly describe the original classical theory.