分野別セミナー

Abstract:
In physical systems one is often interested in knowing if the ground state is unique or not. If one wants to prove such results for all values of some coupling constant then one needs to use Perron-Frobenius type arguments and positive cones. The main tool for establishing such positivity and also certain energy inequalities is the celebrated Feynman-Kac formulas which arise in stochastic analysis. In this talk I combine positivity and probability theory in a new way to prove uniqueness of ground states and energy inequalities in cases where Feynman-Kac formulas are not available. Especially we shall see how these techniques can be applied to a translation invariant models from non relativistic quantum field theory, to show non trivial properties about their spectra.