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

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

2001-03-14

arxiv.org/abs/gr-qc/0103048v1

Class.Quant.Grav. 18 (2001) 1767-1786

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, LaTex, no figures, to appear in Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/18/9/311

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.

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