NEW METHOD IN THE STUDY OF RELATIVISTIC BOUND STATES

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[I] It is a very difficult problem to directly derive properties of hadrons from QCD.Recently there has been a growing interest in Hamiltonian field theory quantized on the light cone as a novel way of investigating bound states. The vacuum in light-cone quantization is extremely simple, and thus the theory has non-relativistic features.(1) By applying the Tamm-Dancoff approximation to 2-dimensional QED quantized on the light cone, we investigated the two-and three-meson bound states. We obtained intuitive pictures of these states by exploiting the wave functions. We furthermore showed how the theta vacuum of the 2-dimensional QED, the simplest vacuum structure, is related to the zero mode of the gauge field.(2) We formulated a renormalization group transformation for a 4-dimensional scalar field theory by using the Bloch-Horowitz effective Hamiltonian. We investigated the phase structure and the relation to the spontaneous symmetry breaking (Harada, Yahiro et al).[II] Theta term in lattice gauge theory leads to complex valued Boltzmann weight in Euclidean space time and can not be a probability weight. Character expansion method based on the orthogonal property of irreducible characters plays a powerful role to investigate the phase structure. Topological charge distribution can be evaluated and the Fourier transform leads to the partition function (Imachi et al).[III] A.The path integral for a harmonic oscillator is known to be given exactly from the saddle point method. Semi-classical approximation in quantum mechanics on Grassmann manifolds is shown to lead to an exact results too. B.A deep investigation on the gauge invariance is made. It will be helpful to understand quark confinement mechanism (Kashiwa et al).