Mathematical Studies on Systems of Particles Interacting with Quantum Fields

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Head investigator(1) Spectral analysis has been made for the Hamiltonian H of a quantum system of a Dirac particle-a relativistic charged particle with spin 1/2-interacting with the quantized radiation field, where the Dirac particle is in an external potential V.The following have been proved : (i) existence of a physically natural self-adjoint extension of H which is connected with the charge conjugation and parity invariance of the external potential V.(ii) For a reasonable class of V, H is essentially self-adjoint.(iii) In the case V=0, H has a direct integral decomposition H=∫^<【symmetry】>_<R^3> H (p) dp.(2) A general structure of the essential spectrum of a class of Hamiltonians which describe particle-field interactions has been clarified.(3) Detailed analysis has been made on the existence or the absence of ground states of the generalized spin boson model.(4) The massless Nelson model has been considered in a non-Fock representation and the existence of a ground state of it has been established.Investigators(a) Existene of a global solution of nonlinear elastic waves (Agemi)(b) Studies on the Rohlin property for automorphisms of general non-commutative shifts (Kishimoto)(c) Studies on asymptotic behaviors of partial autocorrelation functions of stationary processes (Inoue)