Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Description

We propose a supergeometric model describing measurements and dynamics of physical systems with both continuous and discrete degrees of freedom. The model treats time on the same footing as other physical degrees of freedom. Our geometric data is not only quite minimal viz. a supersymplectic manifold with odd dimensional body, but canonically incorporates dynamics. A measurement theory must come with a notion of states, observables and expectations. Our states are quantum mechanical, observable are functions on the supersymplectic manifold and expectation values are given by a fiberwise Hodge pairing. We also study statistics of superobservables using a distinguished set of non-homogeneous superfunctions labelled by elements of a free Boolean algebra. We find an interpretation of supermoments in terms of certain truncated spectral statistics. We conclude with some promising future directions such as applying supermeasurement theory to the SIC POVM existence problem.