Math Physics Seminar – Professor Wayne Polyzou | Physics and Astronomy

Professor Wayne Polyzou; University of Iowa, Department of Physics and Astronomy

Completeness and complex probabilities in descrete systems

Abstract: I discuss a general real-time path integral treatment of discrete systems motivated by Jorgensen and Nathanson’s treatment of real time path integrals based on complex probabilities.  For imaginary times in the continuum theory there is a path measure that can be alternatively considered as a probability measure; while for real time there is no countably additive measure on the cylinder sets of paths, the probability interpretation survives if the notion of probability is properly extended to complex probabilities.  In the discrete case the complex probability arises from the completeness relation, there are no Fresnel integrals, and the space of paths are cylinder sets of paths that take on discrete values of complementary pairs of observables at different time slices.  The cylinder sets of discrete paths are in 1-1 correspondence with ordered sequences of transition amplitudes involving complementary pairs of operators.  I will discuss a trivial application to quantum field theory.

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