Smooth Loop Quantum Geometries and the Emergence of an Effective Quantum Field Theory
Speaker(s): Tim Koslowski
Abstract: We construct a representation for the Weyl-algebra underlying Loop Quantum Gravity constructed from a diffeomorphism variant state, which corresponds to a ''condensate'' of Loop Quantum Geometry, resembling a static spatial geometry. We calculate the gauge- and diffeomorphism invariant Hilbert space representation and find that the expectation values of the geometric operators take essentialy classical values plus quantum corrections. Having an essential geometry at our disposal we construct a scale dependent asymptotic morphism into a one parameter family of scale dependent lattice gauge theories, where scale separates the essential geometry (which arises by integrating short distance physics out) and a low energy effective theory (which is described as degrees of freedom in the lattice gauge theory). It turns out that this Hilbert space contains unexpected effective degrees of freedom.
Date: 16/08/2007 - 4:30 pm
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