Quantum evolution of the Universe from $τ=0$ in the constrained quasi-Heisenberg picture

Details Quantum evolution of the Universe from $τ=0$ in the constrained quasi-Heisenberg picture Quantum evolution of the Universe from $τ=0$ in the constrained quasi-Heisenberg picture

2005-02-10

arxiv.org/abs/gr-qc/0502044v5

Proc. VIIIth International School-seminar "The Actual Problems of Microworld Physics" (Gomel), Dubna 2007, v. I, p. 208-222.

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Lecture at the VIIIth International School-seminar "The Actual Problems of Microworld Physics", Gomel, Belarus, July 25-August

Scientific paper

The Heisenberg picture of the minisuperspace model is considered. The suggested quantization scheme interprets all the observables including the Universe scale factor as the (quasi)Heisenberg operators. The operators arise as a result of the re-quantization of the Heisenberg operators that is required to obtain the hermitian theory. It is shown that the DeWitt constraint H=0 on the physical states of the Universe does not prevent a time-evolution of the (quasi)Heisenberg operators and their mean values. Mean value of an observable, which is singular in a classical theory, is also singular in a quantum case. The (quasi)Heisenberg operator equations are solved in an analytical form in a first order on the interaction constant for the quadratic inflationary potential. Operator solutions are used to evaluate the observables mean values and dispersions. A late stage of the inflation is considered numerically in the framework of the Wigner-Weyl phase-space formalism. It is found that the dispersions of the observables do not vanish at the inflation end.

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