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Infinite multiplets in quantum field theory
ANNALS
OF PHYSICS:
49,
Abstracts
171 (1968)
of Papers
to Appear
in Future
Issues
Infinite Multiplets in Quantum Field Theory. CAO CHI, DAO VONG DYC, AND NGUYEN VAN HIEU. Joint Institute for Nuclear Research, Laboratory of Theoretical Physics, Moscow, U.S.S.R. This paper treats some essential results obtained by the authors in quantum field theory with infinite multiplets. The explicit expression of the matrix of finite Lorentz transformation is found. The interaction of infinite multiplets is studied and its specific properties are shown. The quantization of fields with infinite multiplets is considered and the existence of big free local fields with normal connection between spin and statistics is shown. The generalized Feynman rules are formulated. Method of Construction of the Green’s Flmctions in Momentum Space for Unrenormaiizable Interactions. M. K. VOKOV. Joint Institute for Nuclear Research, Dubna, U.S.S.R. A unitary method is developed for constructing the Fourier transform of the two-point Green’s functions in local and nonlocal theories with unrenormalizable interactions. The spectral representations of these functions are derived. It is shown that the functions considered have a logarithmic branch point with respect to g for g = 0 in the momentum space. The Talmi Transformation for Different Particles-A Complete Construction and New Results. A. GAL. Laboratory for Nuclear Science & Physics Department, M.I.T., Cambridge, Massachusetts. The transformation from single-particle coordinates to relative and center-of-mass coordinates for two particles moving in a common harmonic-oscillator potential well is generalized to include the case of different single-particle frequencies. The physical implications, particularly for hypernuclear structure calculations, are pointed out. Explicit expressions for the transformation matrix are obtained which show the group-theoretical structure of the transformation. A generalization to n-dimensional harmonic oscillators is straightforward. As a byproduct the Clebsch-Gordan series for a direct product of two symmetric SU(n) irreducible representations is derived. Phonons Treated as Renormalized Einstein Phorwns. H. C. BOLTON AND G. J. COOMBS. Physics Department, Monash University, Clayton, Victoria, Australia. The interaction between localized Einstein phonons is shown by a Green’s function method to give rise to the familiar one-dimensional dispersion relation for the frequency of the phonons of the whole lattice. The discussion parallels a recent paper of Mattuck who summed the diagrams exactly. The chain of coupled equations for the Green’s function terminates and has an exact solution. The familiar ensemble-averaged occupation number follows from the spectral density. Unified Theory of CP-Conserving and -Violating Weak Interactions. SUSUMU OKUBO. Department of Physics and Astronomy, University of Rochester, Rochester, New York. Assuming the intermediate vector meson being a Yang-Mill field, one can treat all weak interaction phenomena involving both CP-conserving and -violating processes in a uni8ed manner. In this theory, the weak interaction violates CP maximally. Also, a notion of the weak W(3) space, in contrast to the ordinary hadronic SU(3) space, has been introduced.
171
Printed
in B&ion
OF PHYSICS:
49,
Abstracts
171 (1968)
of Papers
to Appear
in Future
Issues
Infinite Multiplets in Quantum Field Theory. CAO CHI, DAO VONG DYC, AND NGUYEN VAN HIEU. Joint Institute for Nuclear Research, Laboratory of Theoretical Physics, Moscow, U.S.S.R. This paper treats some essential results obtained by the authors in quantum field theory with infinite multiplets. The explicit expression of the matrix of finite Lorentz transformation is found. The interaction of infinite multiplets is studied and its specific properties are shown. The quantization of fields with infinite multiplets is considered and the existence of big free local fields with normal connection between spin and statistics is shown. The generalized Feynman rules are formulated. Method of Construction of the Green’s Flmctions in Momentum Space for Unrenormaiizable Interactions. M. K. VOKOV. Joint Institute for Nuclear Research, Dubna, U.S.S.R. A unitary method is developed for constructing the Fourier transform of the two-point Green’s functions in local and nonlocal theories with unrenormalizable interactions. The spectral representations of these functions are derived. It is shown that the functions considered have a logarithmic branch point with respect to g for g = 0 in the momentum space. The Talmi Transformation for Different Particles-A Complete Construction and New Results. A. GAL. Laboratory for Nuclear Science & Physics Department, M.I.T., Cambridge, Massachusetts. The transformation from single-particle coordinates to relative and center-of-mass coordinates for two particles moving in a common harmonic-oscillator potential well is generalized to include the case of different single-particle frequencies. The physical implications, particularly for hypernuclear structure calculations, are pointed out. Explicit expressions for the transformation matrix are obtained which show the group-theoretical structure of the transformation. A generalization to n-dimensional harmonic oscillators is straightforward. As a byproduct the Clebsch-Gordan series for a direct product of two symmetric SU(n) irreducible representations is derived. Phonons Treated as Renormalized Einstein Phorwns. H. C. BOLTON AND G. J. COOMBS. Physics Department, Monash University, Clayton, Victoria, Australia. The interaction between localized Einstein phonons is shown by a Green’s function method to give rise to the familiar one-dimensional dispersion relation for the frequency of the phonons of the whole lattice. The discussion parallels a recent paper of Mattuck who summed the diagrams exactly. The chain of coupled equations for the Green’s function terminates and has an exact solution. The familiar ensemble-averaged occupation number follows from the spectral density. Unified Theory of CP-Conserving and -Violating Weak Interactions. SUSUMU OKUBO. Department of Physics and Astronomy, University of Rochester, Rochester, New York. Assuming the intermediate vector meson being a Yang-Mill field, one can treat all weak interaction phenomena involving both CP-conserving and -violating processes in a uni8ed manner. In this theory, the weak interaction violates CP maximally. Also, a notion of the weak W(3) space, in contrast to the ordinary hadronic SU(3) space, has been introduced.
171
Printed
in B&ion