文档介绍：Modern Nonlinear Optics, Part 2, Second Edition: Advances in Chemical Physics, Volume 119.
Edited by Myron W. Evans. Series Editors: I. Prigogine and Stuart A. Rice.
Copyright # 2001 John Wiley & Sons, Inc.
ISBNs: 0-471-38931-5 (Hardback); 0-471-23148-7 (Electronic)
ELECTRODYNAMICS AND TOPOLOGY
PATRICK CORNILLE
Advanced ic Systems, ., 4 Rue de la Pommeraie,
78470 St. Re´my-Le`s-Chevreuse, France
CONTENTS
I. Introduction
II. Helmholtz Theorem
A. Integral Spatial Solution
B. Fourier Analysis
C. Integral Solution in Spacetime
D. Application to Maxwell–Ferrier Equations
III. Study of Rotational Fields
A. Study of Beltrami and Trkal Fields
B. Force-Frece Field and Virial Theorm
C. Ordinary Fields and the Superposition Principle
D. Hansen position and Beltrami Field
E. Hansen position in Different Coordinate Systems
1. Case of Cartesian Coordinates
2. Case of Cylindrical Coordinates
IV. Investigation of Topological Effects in Physics
A. Study of Helicity
B. Temporal Derivation of Helicity
C. Topological Effect Associated with Voltage Measurement
D. The Aharonov–Bohm Effect
Acknowledgments
References
I. INTRODUCTION
Topology is the discipline within mathematical science dealing with the intuitive
concepts of continuity and limits. This discipline is posed of several
distinct fields of interest. Within the scope of this particular chapter, we shall
investigate differential topology, with the understanding that this discipline aims
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at studying both the classification of surfaces and the problems usually associated
with knots. The theory of knots is now reaching the general public interest, as
illustrated by an ever-growing list of cover stories, special issues, and reports
published in popular science literature on this particularly ‘‘knotty’’ subject
[1–4]. Of course, this chapter does not explore every aspect of knot physics, but
parts of it only.
More specifically, we shall fi