The "extended phase space" approach to quantum geometrodynamics: what can it give for the development of quantum gravity?
T. P. Shestakova
备注：
12 pages, talk presented at the III Stueckelberg Workshop on Relativistic Field Theories, Pescara, Italy, July 2008
发表信息：
Proceedings of the 3rd Stueckelberg Workshop on Relativistic Field Theories, eds. N. Carlevaro, R. Ruffini and G. V. Vereshchagin, Cambridge Scientific Publishers, 2010, P. 293 - 301
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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Revisiting light propagation over (loop) quantum Universe
Faculty of Mathematics and Computer Science, Transilvania University（特兰西瓦尼亚大学数学与计算机科学学院）；University of Wrocław, Faculty of Physics and Astronomy, Institute of Theoretical Physics（弗罗茨瓦夫大学物理与天文学学院理论物理研究所）
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame as a differential manifold with an affine connection results in separation of the respective contributions of inertial and gravitational fields represented by the affine connection and the tensor of nonmetricity within the Levi-Civita connection of GR. Resulting decomposition of the Einstein curvature tensor into affine and nonmetric parts allows to recast …
A brief review of main features of the new approach named ``quantum geometrodynamics in extended phase space'' is given and its possible prospects are discussed. Gauge degrees of freedom are treated as a subsystem of the Universe which affects the evolution of the physical subsystem. Three points can be singled out when the gauge subsystem shows itself as a real constituent of the Universe: a chosen gauge condition determines the form of equation for the physical part of wave function, the form of density matrix and the measure in physical subspace. An example is considered when a physically r…
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Mapping-class groups of 3-manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries, their inequivalent unitary irreducible representations should give rise to a complex superselection structure. This highlights certain aspects of spatial diffeomorphism invariance that to some degree seem physically meaningful and which persist in all approaches based on smooth 3-manifolds, like geometrodynamics and loop quantum gravity. We also attempt to give …
