Mathematical Studies on Systems of Particles Interacting with Quantum Fields

(1)对Dirac粒子（自旋为1/2的相对论性带电粒子）与量子化辐射场相互作用的量子系统的哈密顿量H进行了谱分析，其中Dirac粒子处于外部势v。(1)存在与外部势V的电荷共轭和宇称不变性有关的H的物理自然自伴随扩展。(2)对于一个合理的V类，H本质上是自伴随的。（iii）当V=0时，H具有直接积分分解H=∫^<【对称】>_<R^3> H (p) dp。(2)阐明了描述粒子场相互作用的一类哈密顿量的基本谱的一般结构。(3)对广义自旋玻色子模型基态的存在与否进行了详细的分析。(4)考虑了非fock表示下的无质量Nelson模型，并确定了其基态的存在。研究人员(a)非线性弹性波整体解的存在性（Agemi）(b)一般非交换位移自同构的Rohlin性质的研究（Kishimoto）(c)平稳过程的部分自相关函数的渐近行为的研究（Inoue）

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)