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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 9: Quantengravitation (joint session MP/GR)

MP 9.2: Vortrag

Mittwoch, 20. März 2019, 17:40–18:00, HS 4

Towards Gaussian states for the holonomy-flux Weyl algebra — •Robert Seeger — Institut für Quantengravitation, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)

An important challenge in loop quantum gravity is to find semiclassical states. This is difficult because states in the Hilbert space are excitations over a vacuum in which geometry is highly degenerate. Additionally, fluctuations are distributed very unevenly between configuration and momentum variables in this state. Coherent states that have been proposed to balance the uncertainties more evenly can, up to now, only do this for finitely many degrees of freedom. Our work is motivated by the desire to obtain Gaussian states that encompass all degrees of freedom. To implement this idea mathematically we reformulate the U(1) holonomy-flux algebra in any dimension as a Weyl algebra, and discuss generalisations to SU(2). We then define and investigate a new class of states on these algebras which behave like quasifree states on momentum variables.