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Nonlinear wave mechanics
ANNALS
OF PHYSICS
99,
Abstracts
229-230 (1976)
of Papers
to Appear
in Future
Issues
Wave Mechanics. Iwo BIALYNICKI-BIRULA. Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, and Institute of Theoretical Physics, Warsaw University 00-681 Warsaw, Poland; AND JERZY MYCIELSKI. Institute of Theoretical Physics, Warsaw University 00-681 Warsaw, Poland.
Nonlinear
Nonlinear wave mechanics is constructed, based on Schrodinger-type equation with nonlinearity --b$ In j 4 12.This nonlinearity is selected by assuming the factorization of wavefunctions for composed systems. Its most attractive features are: existence of the lower energy bound and validity of Plan&s relation E = tiw. In any number of dimensions, soliton-like solutions (gaussons) of our equation exist and move in slowly varying fields like classical particles. The Born interpretation of the wavefunction is consistent with logarithmic nonlinearity and we tentatively estimate the order of magnitude of the universal constant 6. N-N Potential. W. T. NUTT. Department of Physics and Institute for Nuclear Theory, Brooklyn College of the City University of New York, Brooklyn, New York 11210.
A Meson-Exchange
A meson-theoretic model of the intermediate range nucleon-nucleon potential is presented with emphasis placed on the two-pion exchange contribution. The Bethe-Salpeter equation is reduced, by the Blankenbecler-Sugar technique, to a Lippmann-Schwinger equation, from which an approximate non-local, energy-dependent potential is obtained. The nucleon-antinucleon pair contribution, which plagues meson-theoretical two-pion calculations, is suppressed by the complex poles of the one-nucleon Green’s function. The importance of the retention of the explicit energy dependence of the potential is demonstrated by calculating the off-shell scattering matrices. The potential is presented in a linearized (in energy) form with the core region adjusted to produce a fit to low energy data. Theory for Pion-Nucleus Interactions. L. S. KISSLINGER. Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 ; AND W. L. WANG. Argonne National Laboratory, Argonne, Illinois 60439.
The Isobar-Doorway
Pionnucleus scattering and reactions are treated in a theory which explicitly introduces the pion-nucleon resonances. Using a separation in Hilbert Space, doorway states of isobarnuclear systems are introduced and nonresonant processes are clearly separated from resonance interactions. With one choice of doorway states a multiple scattering series is derived which corresponds to the conventional theory with binding energy and other corrections included. When another choice the isobar doorway model is derived, with parameterization explicitly related to specific dynamic effects, our framework provides a phenomenological model for treating mesonnucleus interactions to all orders. Moreover, the parameters of the model have clear theoretical significance which can extend our knowledge of strong interactions physics. A numerical study is given for elastic scattering. An Energy-Momentum
Tensor
in Gauge
Theories.
SATISH
D.
JOGLEKAR,
Institute for Advanced
Study, Princeton, New Jersey 08540. We consider the renormalization of the twist two, dimension four gauge invariant operator 0;; = -F,,F,, - g,zO. By using the general theory of renormalization of gauge invariant
229 Copyright All rights
8 1916 by Academic Press, Inc. of reproduction in any form reserved.
OF PHYSICS
99,
Abstracts
229-230 (1976)
of Papers
to Appear
in Future
Issues
Wave Mechanics. Iwo BIALYNICKI-BIRULA. Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, and Institute of Theoretical Physics, Warsaw University 00-681 Warsaw, Poland; AND JERZY MYCIELSKI. Institute of Theoretical Physics, Warsaw University 00-681 Warsaw, Poland.
Nonlinear
Nonlinear wave mechanics is constructed, based on Schrodinger-type equation with nonlinearity --b$ In j 4 12.This nonlinearity is selected by assuming the factorization of wavefunctions for composed systems. Its most attractive features are: existence of the lower energy bound and validity of Plan&s relation E = tiw. In any number of dimensions, soliton-like solutions (gaussons) of our equation exist and move in slowly varying fields like classical particles. The Born interpretation of the wavefunction is consistent with logarithmic nonlinearity and we tentatively estimate the order of magnitude of the universal constant 6. N-N Potential. W. T. NUTT. Department of Physics and Institute for Nuclear Theory, Brooklyn College of the City University of New York, Brooklyn, New York 11210.
A Meson-Exchange
A meson-theoretic model of the intermediate range nucleon-nucleon potential is presented with emphasis placed on the two-pion exchange contribution. The Bethe-Salpeter equation is reduced, by the Blankenbecler-Sugar technique, to a Lippmann-Schwinger equation, from which an approximate non-local, energy-dependent potential is obtained. The nucleon-antinucleon pair contribution, which plagues meson-theoretical two-pion calculations, is suppressed by the complex poles of the one-nucleon Green’s function. The importance of the retention of the explicit energy dependence of the potential is demonstrated by calculating the off-shell scattering matrices. The potential is presented in a linearized (in energy) form with the core region adjusted to produce a fit to low energy data. Theory for Pion-Nucleus Interactions. L. S. KISSLINGER. Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 ; AND W. L. WANG. Argonne National Laboratory, Argonne, Illinois 60439.
The Isobar-Doorway
Pionnucleus scattering and reactions are treated in a theory which explicitly introduces the pion-nucleon resonances. Using a separation in Hilbert Space, doorway states of isobarnuclear systems are introduced and nonresonant processes are clearly separated from resonance interactions. With one choice of doorway states a multiple scattering series is derived which corresponds to the conventional theory with binding energy and other corrections included. When another choice the isobar doorway model is derived, with parameterization explicitly related to specific dynamic effects, our framework provides a phenomenological model for treating mesonnucleus interactions to all orders. Moreover, the parameters of the model have clear theoretical significance which can extend our knowledge of strong interactions physics. A numerical study is given for elastic scattering. An Energy-Momentum
Tensor
in Gauge
Theories.
SATISH
D.
JOGLEKAR,
Institute for Advanced
Study, Princeton, New Jersey 08540. We consider the renormalization of the twist two, dimension four gauge invariant operator 0;; = -F,,F,, - g,zO. By using the general theory of renormalization of gauge invariant
229 Copyright All rights
8 1916 by Academic Press, Inc. of reproduction in any form reserved.