A treatise on the magnetic vector potential. ([2020])

• Record Type: Book
• Further Information: Note: Kristján Óttar Klausen.
• Authors: Klausen, Kristján Óttar
• Contents: Intro -- 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
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2020
• Extent: 1 online resource (129 pages)
• Subjects: 535.14; Electromagnetic theory; Classical Electrodynamics; Optics, Lasers, Photonics, Optical Devices; Electronic books
• Languages: English
• ISBNs: 9783030522223; 3030522229
• Related ISBNs: 3030522210; 9783030522216
• Notes: Note: Includes bibliographical references.; Note: Description based on online resource; title from digital title page (viewed on October 12, 2020).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.