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arXiv · 0810.4031

The "extended phase space" approach to quantum geometrodynamics: what can it give for the development of quantum gravity?

T. P. Shestakova
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Abstract

The talk is devoted to the "extended phase space" approach to Quantum Geometrodynamics. The premises that have led to the formulation of this approach are briefly reviewed, namely, non-trivial topology of the Universe which implies the absence of asymptotic states, in contrast to situations one usually deals in ordinary quantum field theory; parametrization noninvariance in the Wheeler - DeWitt theory; the problem of time and the absence of dynamical evolution. Then we discuss the main features of the approach: Hamiltonian dynamics in extended phase space, gauge-dependent Schrodinger equation for the wave function of the Universe, the description of quantum Universe from the viewpoint of observers in a wide enough class of reference frames. After all, we analyse problems arising in this approach: the structure of Hilbert space in Quantum Geometrodynamics, the relations between solutions for the wave function of the Universe corresponding to various reference frames, properties of a medium to be necessary to fix a reference frame, the transition to classical limit.

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T. P. Shestakova. 2008-10-22. The "extended phase space" approach to quantum geometrodynamics: what can it give for the development of quantum gravity?. https://arxiv.org/abs/0810.4031

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