Symmetries in Physics

Inhaltsverzeichnis

• 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 Resumé 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 Grüneisen 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-à-vis Those in Optics.
• 22.1 Introduction.
• 22.2 The phase space of mechanics and that of optics.
• 22.3 Transformations in mechanical vis-à-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.