Hamburg 2016 – wissenschaftliches Programm

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GR: Fachverband Gravitation und Relativitätstheorie

GR 2: Quantum Gravity I

GR 2.2: Vortrag

Montag, 29. Februar 2016, 11:40–12:00, VMP6 HS A

Semiclassical perturbation theory in Loop Quantum Gravity — •David Winnekens and Kristina Giesel — University of Erlangen-Nürnberg, Institute for Quantum Gravity, Theoretical Physics III, Staudtstr. 7, 91058 Erlangen

The volume operator plays a pivotal role in the quantum dynamics of Loop Quantum Gravity, yet its full spectrum is unknown. This also affects a semiclassical analysis of the theory since that requires computing semiclassical expectation values of dynamical operators, which themselves involve the volume operator. Within the context of Algebraic Quantum Gravity [1] – a model formulated in the framework of Loop Quantum Gravity –, a formalism called semiclassical perturbation theory was developed, which allows calculating these semiclassical expectation values perturbatively as a power series in ℏ.

This talk presents an application of this formalism to the operator of the inverse scale factor, which is an important ingredient for the dynamics of quantum cosmological models. In [2], a semiclassical analysis of this operator has been performed via substituting SU(2) by U(1)³. In this case, the volume operator simplifies drastically. With the work presented in this talk, the analysis of [2] can be generalized to the full SU(2)-case.

[1] Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory, K. Giesel, T. Thiemann, Class.Quant.Grav.24:2565-2588, 2007 [2] On (Cosmological) Singularity Avoidance in Loop Quantum Gravity, J. Brunnemann, T. Thiemann, Class.Quant.Grav.23:1395-1428, 2006