Generalized Hamiltonian dynamics of Friedmann cosmology with scalar and spinor matter source fields (Q2724808)

The classical and quantum dynamics of the Friedmann-Robertson-Walker (FRW) universe with a massless scalar and massive fermion matter field as a source is discussed within 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, \(k=0,\pm 1\), 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 timelike Killing vector fields in FRW spacetime to the existence of the time-independent Hamiltonian and the corresponding notion of conserved energy is discussed. The extended quantization with the Wheeler-de Witt 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.