Hokkaido Mathematical Journal

MIYAO Tadahiro, SASAKI Itaru,

Stability of discrete ground state.

Hokkaido Mathematical Journal, 34 (2005) pp.689-717




We present new criteria for a self-adjoint operator to have a ground state. Although the proof which we give is easy, it has many applications. And in various models, it is easy to check the criteria. As an application, we consider models of "quantum particles" coupled to a massive Bose field and prove the existence of a ground state of them, where the particle Hamiltonian does not necessarily have compact resolvent.

Uncontrolled Keywordsground state, discrete ground state, generalized spin-boson model, Fock space,Derezi\'nski-G\'erard model