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

TL;DR

This paper reviews the extended phase space approach to quantum geometrodynamics, addressing key issues like topology, gauge dependence, and the problem of time, and explores its implications for quantum gravity development.

Contribution

It introduces a Hamiltonian dynamics framework in extended phase space with a gauge-dependent Schrödinger equation for the Universe's wave function, offering new perspectives on quantum gravity.

Findings

Analysis of gauge-dependent wave functions in different reference frames

Discussion of Hilbert space structure in quantum geometrodynamics

Insights into classical limit transition in the extended phase space approach

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.