Spectral Properties for Hamiltonians of Weak Interactions

Abstract

We present recent results on the spectral theory for Hamiltonians of the weak decay. We discuss rigorous results on self-adjointness, location of the essential spectrum, existence of a ground state, purely absolutely continuous spectrum and limiting absorption principles. The last two properties heavily rely on the so-called Mourre Theory, which is used, depending on the Hamiltonian we study, either in its standard form, or in a more general framework using non self-adjoint conjugate operators.

Mathematics Subject Classification (2010). 47B25, 81Q10, 81T10, 83C47.