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Gaussian measures and representations of the holonomy-flux algebra

Sep 22
Group Seminar
10:00 am o'clock to 11:00 am o'clock
Stefan Nekovar (IQG FAU Erlangen)
SR 02.729

Gaussian path integrals play an important role for free quantum field theories, and for the perturbative treatment of interacting quantum field theories. We give a general definition of a Gaussian measure over (Abelian) connections, and study their properties. Then we investigate the absolute continuity of Gaussian measures with respect to representations of the holonomy-flux Weyl algebra for $U(1)$. This shows that for a large subclass, the lengthlike Gaussian measures, there are no representations, where the fluxes can be implemented unitarily.