Perturbation theory of boson dynamical systems

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Abstract
Dynamical evolutions of boson (spin-boson and related) systems based on the widely used canonical commutation relations C* algebra have a shortcoming. The dynamical group is not pointwise norm-continuous and therefore cannot be perturbed by a (bounded self-adjoint) element of the underlying abstract C* algebra. Hence it is necessary to define notions like 'invariant state', 'ground state', 'KMS state', etc. with respect to the perturbed dynamics in suitable Hilbert space representations. Here the original dynamical system is supplemented by an auxiliary pointwise norm-continuous dynamical system in such a way that invariant states of the original system correspond to invariant states of the auxiliary system. This bijective correspondence is sequentially continuous and preserves the KMS (ground state) characterizing conditions. As a typical application it is verified that Spohn's ground states of the spin-boson model (1989) (arising as a temperature to zero limit of thermic equilibrium states) are ground states in the algebraic sense, i.e. are eigenstates of the respective (Gel'fand-Naimark-Segal) Hamiltonian with an eigenvalue at the lower end of the Hamiltonian spectrum.

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