Topological Effects in Quantum Mechanics

Among the subjects covered in this volume are the topological effects of quantum mechanics, including Bohm-Aharonov and Aharonov-Casher effects and their generalisations; the toroidal moments, anapoles and their generalisations; the numerical investigation of Tonomura experiments testing the foundat...

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Main Author: Afanasiev, G.N.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1999, 1999
Edition:1st ed. 1999
Series:Fundamental Theories of Physics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 7.1 An Elementary Exposition of the Bohm–Aharonov Effect
  • 7.2 Attempts at Proving the Non-Existence of the B–A Effect
  • 7.3 Scattering of Charged Particles on Two Infinite Cylindrical Solenoids
  • 7.4 Scattering of Charged Particles by a Toroidal Solenoid
  • 7.5 On the Super-Current Arising in a Superconducting Ring
  • 7.6 The Time-Dependent Bohm–Aharonov Effect
  • 7.7 Scattering of Charged Particles in an Ideal Multiply Connected Spacial Region
  • 7.8 On the Alternative Interpretation of the Bohm–Aharonov Effect
  • 7.9 The B–A Effect for Bound States
  • 7.10 Quantum Impenetrability and Bohm–Aharonov Scattering
  • 7.11 The Aharonov-Casher Effect
  • 8 Topological Effects for the Free Electromagnetic Field
  • 8.1 Introduction
  • 8.2 Relativistic Helicity and Its Physical Meaning
  • 8.3 Gauge-Invariant Representation for the Energy of a Weak Gravitational Field
  • 8.4 Photon Densities
  • 8.5 Numerical Results
  • 8.6 On the Ehrenfest–Pauli Objections
  • 4.4 Magnetisations and the Debye Potential Representation
  • 4.5 Physical Meaning of the ? Functions
  • 4.6 Transition to Point-Like Sources
  • 4.7 The Interaction of Charge Densities with an External Field
  • 4.8 Motion of a Toroidal Solenoid in an External Electromagnetic Field
  • 4.9 On the Inversion of the Debye Parametrisation
  • 4.10 Concluding Remarks
  • 5 Electromagnetic Properties of Time-Dependent Solenoids
  • 5.1 Cylindrical Solenoids
  • 5.2 Toroidal Solenoids
  • 5.3 Elementary Time-Dependent Toroidal Sources
  • 5.4 Vector Solutions of the Laplace Equation
  • 6 Radiationless Time-Dependent Charge-Current Sources
  • 6.1 Introduction
  • 6.2 On Radiationless Topologically Non-Trivial Sources of Electromagnetic Fields
  • 6.3 On Current Configurations Generating a Static Electric Field
  • 6.4 On Electric Vector Potentials
  • 6.5 More General Radiationless Sources
  • 6.6 Concluding Remarks Toroidal Radiationless Sources
  • 7 Selected Topological Effects of Quantum Mechanics
  • 1 Introduction
  • 2 Vector Potentials of Static Solenoids
  • 21 Cylindrical Solenoids
  • 2.2 Vector Potential of the Toroidal Solenoid
  • 3 Electromagnetic Properties of Static Solenoids
  • 3.1 Conditions for the Existence of Static Magnetic Solenoids
  • 3.2 Currents, Magnetic Dipoles and Monopoles
  • 3.3 Electric Static Solenoids
  • 3.4 On the Disappearance of the Magnetic Field Inside a Solenoid
  • 3.5 Vector Potentials of Toroidal Solenoids with Different Asymptotic Behaviour
  • 3.6 Solenoids with Non-trivial Helicity
  • 3.7 Electromagnetic Field of a Cylindrical Solenoid Moving Uniformly in a Medium
  • 3.8 Generalised Helmholtz Coils and All That
  • 4 Interaction of Magnetisations with an External Electromagnetic Field and a Generalisation of AmpÈRe’s Hypothesis
  • 4.1 Introduction
  • 4.2 Magnetisation, Toroidalisation, and a Generalisation of Ampère’s Hypothesis
  • 4.3 Interaction with an External Electromagnetic Field
  • 8.7 On the Hegerfeldt Theorem and All That
  • 8.8 Electromagnetic Waves versus Photons
  • 8.9 Discussion
  • 9 Topology of the Vavilov-Cherenkov Radiation Field
  • 9.1 Introduction
  • 9.2 Mathematical Preliminaries
  • 9.3 Electromagnetic Field of a Uniformly Moving Charge on Finite and Infinite Intervals
  • 9.4 Vavilov–Cherenkov Effect and Accelerated Motion of a Charged Particle
  • References