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Production of pions from nucleons by photons
ANN.4LS
OF PHYSICS:
Abstracts
46, 336-337
of
(1967)
Papers
to Appear
in Future
Issues
Nonlocal E$ects in Classical and Quantum Theories. D. WISNIVESKY AND Y. AHARONOV. Belfer Graduate School of Science, Yeshiva University, New York, New York. Quantum effects of electromagnetic potentials are analyzed further. It is shown that other theories, both classical and quantum mechanical, exhibit analogous effects. Examples from classical General Relativity, Yang-Mills theory, and Quantum Field Theory are discussed. It is concluded that effects of this kind are not necessarily quantum mechanical in nature and not necessarily related to the appearance of nongauge-invariant potentials in the formation of the theory.
Production of Pions from N&eons by Photons. MICHAEL G. GUNDZIK, A. P. BALACHANDRAN, P. NARAYANASWAMI, AND F. NICODEMI. High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois. We study the low energy behavior of the S- and P-wave multipoles corresponding to the isoscalar and symmetric isovector amplitudes for the process y + N + N + r using certain current algebraic techniques developed in an earlier paper. All terms up to and including those which are quadratic in the pion momentum are evaluated for the real parts of the multipoles. A comparison of our techniques with those of Chew, Goldberger, Low and Nambu is carried out and some general conjectures regarding the current algebra approach to low energy phenomena are presented. The difficulties encountered in extending this approach to the antisymmetric, isovector photoproduction amplitude are indicated. Finite Range Solutions to the One-Dimensional Inverse Scattering Problena. JOAS CANDIDO PORTINARI. Instituto de Matematica da P.U.C. Rua Marques S. Vicente, Rio de Janeiro, Brazil. The purpose of this paper is to suggest some ideas concerning the obtention of finite range solutions to the so-called one-dimensional inverse scattering problem. A necessary condition on the ratio of the reflection and transmission coefficients is given for the corresponding potential to be cut off on both sides.
Thermal Conductivity in Nonconducting Crystals. J. RANNINGER. Theoretical Physics Division A E R E, Harwell, Didcot., Berkshire, England. The lattice thermal conductivity is studied for monatomic crystal structures in the framework of the theory of linear response functions. The lattice anharmonicity is treated by three phonon-processes only and the simplest nontrivial self-consistent expression for the phonon self-energy is used. This approximation which corresponds to a generalized Peierlsphonon-Boltzmann equation, where repeated random phase approximation is not assumed, is used in a self-consistent evaluation of the energy-current autocorrelation function. Summing an infinite set of ladder-type diagrams, an expression for the conductivity is obtained in terms of a “transport lifetime” replacing the “single-mode relaxation time” commonly used as an approximate description for transport phenomena. This transport lifetime is found to be a modification of the single-mode relaxation time in two ways. Firstly, it describes the 336
OF PHYSICS:
Abstracts
46, 336-337
of
(1967)
Papers
to Appear
in Future
Issues
Nonlocal E$ects in Classical and Quantum Theories. D. WISNIVESKY AND Y. AHARONOV. Belfer Graduate School of Science, Yeshiva University, New York, New York. Quantum effects of electromagnetic potentials are analyzed further. It is shown that other theories, both classical and quantum mechanical, exhibit analogous effects. Examples from classical General Relativity, Yang-Mills theory, and Quantum Field Theory are discussed. It is concluded that effects of this kind are not necessarily quantum mechanical in nature and not necessarily related to the appearance of nongauge-invariant potentials in the formation of the theory.
Production of Pions from N&eons by Photons. MICHAEL G. GUNDZIK, A. P. BALACHANDRAN, P. NARAYANASWAMI, AND F. NICODEMI. High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois. We study the low energy behavior of the S- and P-wave multipoles corresponding to the isoscalar and symmetric isovector amplitudes for the process y + N + N + r using certain current algebraic techniques developed in an earlier paper. All terms up to and including those which are quadratic in the pion momentum are evaluated for the real parts of the multipoles. A comparison of our techniques with those of Chew, Goldberger, Low and Nambu is carried out and some general conjectures regarding the current algebra approach to low energy phenomena are presented. The difficulties encountered in extending this approach to the antisymmetric, isovector photoproduction amplitude are indicated. Finite Range Solutions to the One-Dimensional Inverse Scattering Problena. JOAS CANDIDO PORTINARI. Instituto de Matematica da P.U.C. Rua Marques S. Vicente, Rio de Janeiro, Brazil. The purpose of this paper is to suggest some ideas concerning the obtention of finite range solutions to the so-called one-dimensional inverse scattering problem. A necessary condition on the ratio of the reflection and transmission coefficients is given for the corresponding potential to be cut off on both sides.
Thermal Conductivity in Nonconducting Crystals. J. RANNINGER. Theoretical Physics Division A E R E, Harwell, Didcot., Berkshire, England. The lattice thermal conductivity is studied for monatomic crystal structures in the framework of the theory of linear response functions. The lattice anharmonicity is treated by three phonon-processes only and the simplest nontrivial self-consistent expression for the phonon self-energy is used. This approximation which corresponds to a generalized Peierlsphonon-Boltzmann equation, where repeated random phase approximation is not assumed, is used in a self-consistent evaluation of the energy-current autocorrelation function. Summing an infinite set of ladder-type diagrams, an expression for the conductivity is obtained in terms of a “transport lifetime” replacing the “single-mode relaxation time” commonly used as an approximate description for transport phenomena. This transport lifetime is found to be a modification of the single-mode relaxation time in two ways. Firstly, it describes the 336