Symmetries in physics : proceedings of the international symposium held in honor of Professor Marcos Moshinsky at Cocoyoc, Morelos, México, June 3-7, 1991

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書誌事項

Symmetries in physics : proceedings of the international symposium held in honor of Professor Marcos Moshinsky at Cocoyoc, Morelos, México, June 3-7, 1991

Alejandro Frank, Kurt Bernardo Wolf, editors

Springer-Verlag, c1992

  • : gw
  • : us

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

This volume aims to provide scientists with an overview of the symmetry methods applied to molecular and nuclear physics, particle physics, decay processes and phase space dynamics. It explores how symmetrical considerations are applied to 20th-century physics.

目次

  • 1 Group Theory and the Harmonic Oscillator: The Work of Marcos Moshinsky.- 1.1 Introduction.- 1.2 Schematic theory of nuclear reactions.- 1.3 The Moshinsky brackets.- 1.4 Marcos' harmonic oscillator.- 1.5 Group theory and nuclear structure.- 1.6 Classical canonical transformations and their unitary representation.- 1.7 Rendering accidental degenerancy non-accidental.- 1.8 Collective models.- 1.9 Structure of matter in strong magnetic fields.- 1.10 Relativistic oscillators.- Electronic and Molecular Physics.- 2 Generalizing the BCS Universal Constants to High-Temperature Superconductivity.- 2.1 Introduction.- 2.2 Generalized BCS Tc-formula.- 2.3 Conclusion.- 3 Fermion Clustering in an Exactly- Soluble N-Fermion Model for Hadronic, Nuclear, and Superconductivity Physics.- 3.1 Introduction.- 3.2 Cooper pairing.- 3.3 Conclusions.- 4 The Scattering Approach to Quantum Electronic Transport.- 4.1 Introduction.- 4.2 Two-terminal systems.- 4.3 Beyond the isotropic model.- 4.4 A three-terminal system.- 5 Symmetry-Avoided Crossings and their Role in the Catalytic Activity of Transition Metals.- 5.1 A personal introduction.- 5.2 General introduction.- 5.3 Method.- 5.4 Results.- 5.5 Conclusions.- Nuclear Physics.- 6 The Symplectic Model and Potential-Energy Surfaces.- 6.1 Introduction.- 6.2 The pseudo-symplectic model.- 6.3 A procedure to construct a PES.- 6.4 Application to 1224Mg and 92238U.- 6.5 Conclusions.- 7 The SU(3) Generalization of Racah's SU(2j + 1) ? SU (2) Group-Subgroup Embedding.- 7.1 Introduction.- 7.2 Resume of Racah's method.- 7.3 The U(3) ? U(dim[m]) embedding.- 7.4 Racah basis for the Lie algebra of any subgroup G ? U(dim[m]).- 7.5 Zeroes of U(3) Racah coefficients.- 8 Scaling and Universality in the Shock Compression of Condensed Matter.- 8.1 Introduction.- 8.2 Rankine-Hugoniot equations.- 8.3 Universality.- 8.4 The empirical expressions for the pressure and internal energy on the shock Hugoniot.- 8.5 A law of corresponding states: scaling.- 8.6 Formal implicit solution for the pressure on the Hugoniot..- 8.7 Conditions on R(P, V) for a double pole in PH(V).- 8.8 Consistency conditions.- 8.9 The complete equation of state in the strong shock regime.- 8.10 The thermodynamic coefficients, the specific heat and the Gruneisen parameter.- 8.11 A thermodynamic expression for the constant A.- 8.12 Summary of results and conclusions.- 9 Deriving Nuclei from Quarks.- 9.1 Introduction.- 9.2 Boson expansions.- 9.3 Iterative mappings of quark systems.- 9.4 The Bonn quark shell model.- 9.5 Results of test calculations for 16O.- 9.6 Concluding remarks.- 10 Binding Energies of Nuclei and Atoms.- Particles and Relativity.- 11 The Relativistic Oscillator and Mass Formulas.- 12 Relativistic Equations in External Fields.- 12.1 Introduction.- 12.2 The Dirac oscillator, a study case.- 12.3 Extended supersymmetric Hamiltonians.- 12.4 Dirac equation in 3 + 1 dimensions.- 12.5 Susy Dirac equation in 4 + 1 and 2 + 1 dimensions.- 12.6 Beyond supersymmetry.- 12.7 Conclusions.- 13 A Parallelism Between Quantum Gravity and the IR Limit in QCD (Emergence of Hadron and Nuclear Symmetries).- 13.1 Symmetries in Nuclei: the IBM Quadrupolar Algebraics.- 13.2 Gravity-like features in hadron dynamics.- 13.3 Flavor SU(3) is generated by QCD, once the fifth is set aside.- 13.4 "Effective" strong gravity is induced by QCD.- 13.5 The algebraics of hadrons and nuclei (classical and quantum).- 13.6 Hadron systematics.- 13.7 The interacting boson model in nuclei.- 13.8 Quadrupolar symmetries in nuclei.- 14 On Rainich-Misner-Wheeler Conditions in Nonlinear Electrodynamics.- 15 Hamiltonian Formulation of a Simple Covariant Harmonic Oscillator for Bosons and Fermions.- 15.1 Introduction.- 15.2 Light cone Hamiltonian formalism.- 15.3 Covariant harmonic oscillator model for two spin-0 constituents.- 15.4 Covariant harmonic oscillator models for two spin-1/2 constituents.- 15.5 Summary and conclusions.- 15.6 Appendix A.- Symmetry and Decay.- 16 Doorway States in Classical Physics.- 16.1 Introduction.- 16.2 The acoustical model.- 16.3 The mathematical setting.- 16.4 Numerical results.- 16.5 Conclusions.- 17 Resonant States and the Decay Process.- 17.1 Introduction.- 17.2 The nondecay amplitude.- 17.3 Time-dependent Green function and resonant states.- 17.4 Full discrete expansion of g(r,r?
  • t) and A(t).- 17.5 Example.- 17.6 Exact one-level decay formula.- 17.7 Conclusion.- 17.A Appendix: Determination of the residue at the pole of the outgoing Green function.- 18 The Decay Process: An Exactly Soluble Example and its Implications.- 18.1 Introduction.- 18.2 A paradox.- 18.3 The problem.- 18.4 The solution.- 18.5 The behavior of A(K,t) for large times.- 18.6 The behavior of A(K,t) for very short times.- 18.7 Conclusion.- 18.A Appendix.- 19 Moshinsky Functions, Resonances and Tunneling.- 19.1 Introduction.- 19.2 The Moshinsky function.- 19.3 Applications: transient effects.- 19.4 Applications: one-dimensional tunneling.- 19.5 Applications: decay.- 19.6 Applications: resonance scattering.- Phase Space Dynamics.- 20 Nonstationary Oscillator in Quantum Mechanics.- 20.1 Introduction.- 20.2 Linear integrals of motion.- 20.3 "Ground" state and coherent states of the parametric oscillator.- 20.4 Fock states and transition probabilities of the time-dependent oscillator.- 20.5 Invariants and propagator.- 20.6 "Damped" oscillator.- 20.7 Casimir effect and parametric oscillator.- 21 Symmetry and Dynamical Lie Algebras in Classical and Quantum Mechanics.- 21.1 Introduction.- 21.2 Definition and properties of symmetry and dynamical Lie algebras.- 21.3 The case of two-dimensional rotationally-invariant Hamiltonians in classical mechanics.- 21.4 The case of two-dimensional rotationally-invariant Hamiltonians in quantum mechanics.- 21.5 Conclusion.- 22 Canonical Transformations in Mechanics vis-a-vis Those in Optics.- 22.1 Introduction.- 22.2 The phase space of mechanics and that of optics.- 22.3 Transformations in mechanical vis-a-vis optical phase space.- 22.4 The canonical transformations that are specific to optics...- 22.5 Outlook: canonical transformations in wave optics.- Round Table.- 23 Science and Technology in Latin America.- Author index.

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