Nonperturbative analysis of charged-particle-system interacting with a quantum field

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The spectrum of Hamiltonians describing a system of charged particles interacting with a quantum field is nonpertubatively studied. It can be regarded as the spectral analysis of a self-adjoint operator on a tensor product of infinite dimensional Hilbert spaces. Mainly an electron minimally coupled with photons, and the so-called Nelson model are investigated by means of functional analysis and functional integrals. The purpos of the present project is as follows : (1)estimates of the number of bosons in ground states, (2)to prove the tightness of Gibbs measures, (3)estimates of the multiplicity of ground states of a Hamiltonian without cutoffs, (4)the decay of the Green functions of a certain spin model. Our achievements are as follows.For (1)by virtute of an application of asymptotic fields of spectral scattering theory in the quantum field theory we got some results which are submitted as the paper entitledRegularities of ground states in quantum field models (with Arai and Hirokawa)For (2)it is obtained some results for a polaron type model of the Pauli-Fierz model by means of a functional integral representation of a heat semigrounp. The result will be submitted somewhere as soon as possible.For (3)an upper bound of the multiplicity of ground states of a Hamiltonian defined through a quadratic form, which is new as far as we know. It is submitted as the paper entitledMultiplicity of ground states in quantum field modelsWe find that this method can be applied for a generalized spin-boson model.A result concerning (4)is obtained for the so-called O(N)-spin model, and now we are writing a paper for this.Throughout this project we can investigate a mass renormalization of the nonrelativistic QED, and we got some results contrary to a conventional physical claim, which is submitted as the paper entitledMass renormalization in nonrelativistic QED with spin 1/2 (with K.R.Ito)