New vacua and representations for loop quantum gravity
Speaker(s): Bianca Dittrich

Loop quantum gravity is based on a particular choice of  basic observable algebra, given  by Wilson loops and (electric) fluxes.

A first step in the quantization program is to find a quantum representation of this algebra. Such a quantum representation is always based on a vacuum state.


A central achievement of loop quantum gravity is the rigorous construction of such a quantum representation, admitting an action of the diffeomorphism group, by Ashtekar, Lewandowski and Isham. An important theorem states also that under a number of conditions this representation is unique.


This brings LQG into a situation very different from standard quantum field theory, where infinitely many representations do exists and are crucial describing e.g. spontaneous symmetry breaking.


I will discuss a new representation which was recently introduced, that avoids one of the more technical assumptions of the uniqueness theorem. It is based on the vacuum of a (BF) topological field theory, excited states describe defects of this topological field theory.


This brings us to the question whether other representations exist, which (I conjecture) is equivalent to classifying phases and their defects in gauge theories.

Date: 19/03/2015 - 5:00 pm
Tech Note: Not Recorded
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