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GR: Fachverband Gravitation und Relativitätstheorie

GR 6: Quantum Gravity and Quantum Cosmology

GR 6.4: Vortrag

Dienstag, 17. März 2015, 15:00–15:20, H 2013

Quantum Geometrodynamics of Conformal Gravity — •Branislav Nikolic — Institute for Theoretical Physics, Cologne, Germany

In order to study the role of conformal symmetry (symmetry under local Weyl rescaling) at the level of quantum gravity, a toy model of conformally invariant gravitational action described with squared Weyl tensor (Weyl tensor action) is canonically quantized. An analog to the Wheeler-DeWitt equation has been proposed, leading to the formulation of quantum geometrodynamics of conformally invariant gravity. From this, the semiclassical expansion in terms of coupling constant is performed and it has been shown that in the highest order one obtains the Hamilton-Jacobi equation corresponding to the Weyl tensor action, while in the next order one obtains a functional Schroedinger equation, analogously to the case of quantum geometrodynamics of General Relativity. Furthermore, the conformal action is extended to the more physically justified action containing additional Einstein-Hilbert term, that breaks the conformal invariance. Upon performing the semiclassical expansion of the corresponding Wheeler-DeWitt equation with respect to the relative couplings of the two terms, it has been shown that the Einstein-Hamilton-Jacobi equation emerges as a classical limit of the theory. Moreover, the problem of time is discussed at the level of both actions. This opens the door to the formulation of quantum geometrodynamics of the higher derivative gravity theories.