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Relativistic and separable classical Hamiltonian particle dynamics
ANNALS OF PHYSICS135, 416-417 (1981)
Abstracts
of Papers to Appear
in Future
Issues
and Separable Classical Hamiltonian Particle Dynamics. H. SAZDJIAN.Division de Physique Thtorique, Institut de Physique Nucleaire, Universite Paris XI, F-91406 Orsay Cedex, France.
Relativistic
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincart invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light. Pseudo-Spin
and Classical
Correspondence
for
Fermi
Fields.
N.
PAPANICOLAOU. Department of Physics,
Washington University, St. Louis, Missouri 63 130. Quantum theories of N-component Fermi fields are formulated in terms of overcomplete sets of bilocal pseudo-spin operators in analogy with the Holstein-Primakoff theory of ordinary spin systems. Classical constrained Hamiltonian systems arise in the large N limit revealing the semi-classical nature of the large N approximation. Such systems are briefly analyzed in the context of the Gross-Neveu (pw)’ model, where the dynamics of c-number (rather than Grassman) fields governs the semi-classical limit. Self-Stress on a Perfectly Conducting Cylindrical Shell. LESTER L. DERAAD, JR., R&D Associates, P.O. Box 9695, Marina del Rey, California 90291; AND KIMBALL A. MILTON, Department of Physics, The Ohio State University, Columbus, Ohio 43210.
Casimir
We compute the Casimir stress on a perfectly conducting cylindrical shell, due to quantum field fluctuations (zero-point energy) in both the interior and exterior regions, using a Green’s dyadic formulation for the field strengths. To obtain a finite answer, a frequency cutoff must be inserted, but the result is independent of that cutoff. The Casimir stress is found to be attractive, the Casimir energy per unit length for a cylinder of radius a being B = -0.014/a2. the TDHF: A Collision Term from a Random-Matrix Model. P. GRANGE, Centre de Recherches Nucleaires, Strasbourg, France; H. A. WEIDENM~LLER, Max-Planck-Institut fiir Kernphysik, Heidelberg, Federal Republic of Germany; AND G. WOLSCHIN, Institut fur theoretische Physik, Universitlt Heidelberg, Heidelberg, Federal Republic of Germany.
Beyond
The mean-field description of low-energy heavy-ion scattering is extended to include the residual nucleon-nucleon interaction. The collision term is derived from a random-matrix model for this interaction in the weak-coupling limit. Particular attention is paid to justifying the approximations made in terms of the time scales typical of nuclei, and to the conservation of energy and particle number.
416 Copyright 0 1981 by Academic Press, Inc. All rights of reproduction in any form reserved.
Abstracts
of Papers to Appear
in Future
Issues
and Separable Classical Hamiltonian Particle Dynamics. H. SAZDJIAN.Division de Physique Thtorique, Institut de Physique Nucleaire, Universite Paris XI, F-91406 Orsay Cedex, France.
Relativistic
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincart invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light. Pseudo-Spin
and Classical
Correspondence
for
Fermi
Fields.
N.
PAPANICOLAOU. Department of Physics,
Washington University, St. Louis, Missouri 63 130. Quantum theories of N-component Fermi fields are formulated in terms of overcomplete sets of bilocal pseudo-spin operators in analogy with the Holstein-Primakoff theory of ordinary spin systems. Classical constrained Hamiltonian systems arise in the large N limit revealing the semi-classical nature of the large N approximation. Such systems are briefly analyzed in the context of the Gross-Neveu (pw)’ model, where the dynamics of c-number (rather than Grassman) fields governs the semi-classical limit. Self-Stress on a Perfectly Conducting Cylindrical Shell. LESTER L. DERAAD, JR., R&D Associates, P.O. Box 9695, Marina del Rey, California 90291; AND KIMBALL A. MILTON, Department of Physics, The Ohio State University, Columbus, Ohio 43210.
Casimir
We compute the Casimir stress on a perfectly conducting cylindrical shell, due to quantum field fluctuations (zero-point energy) in both the interior and exterior regions, using a Green’s dyadic formulation for the field strengths. To obtain a finite answer, a frequency cutoff must be inserted, but the result is independent of that cutoff. The Casimir stress is found to be attractive, the Casimir energy per unit length for a cylinder of radius a being B = -0.014/a2. the TDHF: A Collision Term from a Random-Matrix Model. P. GRANGE, Centre de Recherches Nucleaires, Strasbourg, France; H. A. WEIDENM~LLER, Max-Planck-Institut fiir Kernphysik, Heidelberg, Federal Republic of Germany; AND G. WOLSCHIN, Institut fur theoretische Physik, Universitlt Heidelberg, Heidelberg, Federal Republic of Germany.
Beyond
The mean-field description of low-energy heavy-ion scattering is extended to include the residual nucleon-nucleon interaction. The collision term is derived from a random-matrix model for this interaction in the weak-coupling limit. Particular attention is paid to justifying the approximations made in terms of the time scales typical of nuclei, and to the conservation of energy and particle number.
416 Copyright 0 1981 by Academic Press, Inc. All rights of reproduction in any form reserved.