A Treatise on the Magnetic Vector Potential 3030522210, 9783030522216

Table of contents :
Foreword by Viðar Guðmundsson
Foreword by Natalia K. Nikolova
Preface
Acknowledgements
Contents
Nomenclature
1 Introduction
References
2 Conceptual Emergence
2.1 Electromagnetic Induction
2.1.1 The Electrotonic State
2.2 Electrokinetic Momentum
2.2.1 Vector Potential
2.2.2 Molecular Vortices
2.3 Elimination for Practical Purposes
2.4 Gauge-Invariance
2.5 Comeback in Quantized Formulation
2.6 The Aharonov-Bohm Effect
2.6.1 Aharonov-Casher Effect
2.7 Geometric Phases
2.8 Gauge Theories
References
3 Mathematical Appearance
3.1 Electromagnetism
3.2 Potential Formulation
3.3 Spacetime Four-Vector Notation
3.4 Variational Approach
3.5 Gauge Invariance in Quantum Electrodynamics
3.5.1 Local Gauge Covariance
References
4 Three Dimensional Solutions
4.1 Line Current
4.2 Method of Solution for the Current Loop
4.2.1 The Dirac Delta Distribution
4.2.2 Green's Function
4.2.3 Eigenfunction Expansion
4.2.4 Bilinear Expansion of Green's Function
4.3 Current Loop
References
5 Theory of Superconductivity
5.1 Perfect Conductivity
5.2 London Equations
5.3 Penetration Depth and the Meissner Effect
5.4 Coherence Length and the Ginzburg-Landau Theory
5.5 Insulator-Superconductor Junction
5.6 Type I Versus Type II Superconductors
5.7 Flux Quantization
5.8 The Josephson Junction
5.9 Microscopic Theory
5.9.1 Second Quantization Technique
5.9.2 BCS Theory
5.10 Bogoliubov-De Gennes Formalism
5.11 Andreev Reflection and the Proximity Effect
5.11.1 The BTK Model
5.11.2 The Superconducting Side
5.11.3 The Normal Metal Side
5.11.4 The Interface
5.11.5 Optical Retro-Reflection
5.12 Superfluidity
5.13 Superfluid Vacuum Theory
5.14 Gauge Invariance in Superconductivity
5.15 Hole Superconductivity and the H-Index
References
6 Applications and Analogies
6.1 Application in Telecommunications
6.2 Hydrodynamics Analogy
6.2.1 Vorticity, Acceleration and Induction
6.2.2 The Navier-Stokes Equation
6.2.3 The Continuity Equation and Incompressible Flow
6.2.4 Irrotational Flow and the Velocity Potential
6.2.5 Table of Comparison
6.3 Population Inversion of Two Dimensional Vortices in a Finite Domain
6.3.1 Entropy
6.3.2 Negative Absolute Temperature
6.3.3 Onsager's System of Parallel Vortices in a Plane
6.3.4 Experiments
6.4 Future Directions
References
7 Final Words
Appendix Appendix
References