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Kinematics at infinite momentum
ANNALS OF PHYSICS:47,4&t-405
Abstracts
of
(1968)
Papers
to
Appear
in
Future
Issues
Kinematics at Infinite Momentum. H. BACRY AND N. P. CHANG. Department of Physics, City College of the City University of New York, New York, New York. In this paper we perform a contraction on the Poincare group which leads to a group isomorphic to the Poincare Group. By “contracting” the canonical representation of the Poincare generators, we show that this iso-Poincare group describes the kinematics of a system of particles all with v, = 1. We give explicitly the behavior of the pI infinite states under finite iso-Poincare transformations. We also give the corresponding transformaion laws under parity and time reversal. As an application, we study a scattering process as viewed by an observer moving with v, = - 1. This leads to a very natural justification of the impact parameter representation of S-matrix element. In conclusion, we give some indications on the covariant generalization of the iso-Poincart group. Ground-State and Low-Excited Properties of Liquid aHe Calculated with a Two-Body Potential. T. W. BURKHARDT. Max-Planck Institute for Physics and Astrophysics, Munich, W. Germany. Although scattering phase shifts reveal that the interaction of two free SHe atoms with the momenta and spins of quasiparticles in liquid aHe is attractive, the experimental spin-averaged effective quasiparticle interaction (F”) defined in Landau’s Fermi-liquid theory is repulsive in liquid JHe. To understand the role of many-body effects in the repulsive interaction, we have calculated the bulk properties of liquid $He using the Bethe-Goldstone method and using Goldstone perturbation theory. The compressibility yields a value for FOE,the angular average of FE. The properties we computed with the Bethe-Goldstone method give good agreement with experiment for effective masses m,* between 1.0 and 1.4 times the true mass. We were unable to determine rng self-consistently. In liquid sHe, three-body correlations are expected to be important. Using techniques developed for nuclear matter by Bethe and his coworkers, we estimated all two- and three-body Goldstone diagrams. The properties we computed are in very good agreement with experiment. Since the net three-body energy is obtained in our calculation by adding repulsive and attractive contributions much larger in absolute value than their sum, these numbers should not be taken too seriously. Three-body diagrams contribute most of the binding energy in our calculation. The three-body repulsive energy is about 60% of the two-body repulsive energy. We describe qualitatively how the Pauli principle helps suppress the contributions of higher clusters. As particles are added to a self-bound many-body system or a system under pressure, the binding energy per particle decreases. Those particles originally present are rearranged into an “excited” state. In both the Bethffioldstone and Goldstone-perturbation-theory calculations, the rearrangement contributions are large enough to make the calculated effective quasiparticle interaction repulsive. A Quarks-on-Springs Model of the Baryons. J. A. SHAPIRO. Department of Physics, University of California, Berkeley, California. The radiative decay of a charged harmonic oscillator is discussed from an algebraic point of view. The possibility of understanding decay widths of baryon towers in an analogous fashion is discussed. A very simple nonrelativistic model of quarks on springs is developed and found to give fairly good agreement to the decays of the d and N& trajectories. 404
Abstracts
of
(1968)
Papers
to
Appear
in
Future
Issues
Kinematics at Infinite Momentum. H. BACRY AND N. P. CHANG. Department of Physics, City College of the City University of New York, New York, New York. In this paper we perform a contraction on the Poincare group which leads to a group isomorphic to the Poincare Group. By “contracting” the canonical representation of the Poincare generators, we show that this iso-Poincare group describes the kinematics of a system of particles all with v, = 1. We give explicitly the behavior of the pI infinite states under finite iso-Poincare transformations. We also give the corresponding transformaion laws under parity and time reversal. As an application, we study a scattering process as viewed by an observer moving with v, = - 1. This leads to a very natural justification of the impact parameter representation of S-matrix element. In conclusion, we give some indications on the covariant generalization of the iso-Poincart group. Ground-State and Low-Excited Properties of Liquid aHe Calculated with a Two-Body Potential. T. W. BURKHARDT. Max-Planck Institute for Physics and Astrophysics, Munich, W. Germany. Although scattering phase shifts reveal that the interaction of two free SHe atoms with the momenta and spins of quasiparticles in liquid aHe is attractive, the experimental spin-averaged effective quasiparticle interaction (F”) defined in Landau’s Fermi-liquid theory is repulsive in liquid JHe. To understand the role of many-body effects in the repulsive interaction, we have calculated the bulk properties of liquid $He using the Bethe-Goldstone method and using Goldstone perturbation theory. The compressibility yields a value for FOE,the angular average of FE. The properties we computed with the Bethe-Goldstone method give good agreement with experiment for effective masses m,* between 1.0 and 1.4 times the true mass. We were unable to determine rng self-consistently. In liquid sHe, three-body correlations are expected to be important. Using techniques developed for nuclear matter by Bethe and his coworkers, we estimated all two- and three-body Goldstone diagrams. The properties we computed are in very good agreement with experiment. Since the net three-body energy is obtained in our calculation by adding repulsive and attractive contributions much larger in absolute value than their sum, these numbers should not be taken too seriously. Three-body diagrams contribute most of the binding energy in our calculation. The three-body repulsive energy is about 60% of the two-body repulsive energy. We describe qualitatively how the Pauli principle helps suppress the contributions of higher clusters. As particles are added to a self-bound many-body system or a system under pressure, the binding energy per particle decreases. Those particles originally present are rearranged into an “excited” state. In both the Bethffioldstone and Goldstone-perturbation-theory calculations, the rearrangement contributions are large enough to make the calculated effective quasiparticle interaction repulsive. A Quarks-on-Springs Model of the Baryons. J. A. SHAPIRO. Department of Physics, University of California, Berkeley, California. The radiative decay of a charged harmonic oscillator is discussed from an algebraic point of view. The possibility of understanding decay widths of baryon towers in an analogous fashion is discussed. A very simple nonrelativistic model of quarks on springs is developed and found to give fairly good agreement to the decays of the d and N& trajectories. 404