School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

LMU Munich

Abstract:Motivated by the axiomatic approach to quantum mechanics, we introduce a certain type of non-linear functionals on the space of observables in classical mechanics, called quasi-states. Quasi-states exist on many symplectic manifolds (these are the phase spaces of classical mechanics). It turns out that a slightly more general kind of functionals, called partial quasi-states, exist on yet more symplectic manifolds and are at the intersection of numerous mathematical disciplines - functional analysis, optimization theory, symplectic geometry, Riemannian geometry, and others. We explain how the methods of symplectic geometry are used in order to construct such functionals and present a few of their applications.

Coffee will be served at 12:00 before the lecture

at Schreiber building 006