Multivectors and Clifford Algebra in ElectrodynamicsWorld Scientific, 1988 - Всего страниц: 316 Clifford algebras are assuming now an increasing role in theoretical physics. Some of them predominantly larger ones are used in elementary particle theory, especially for a unification of the fundamental interactions. The smaller ones are promoted in more classical domains. This book is intended to demonstrate usefulness of Clifford algebras in classical electrodynamics. Written with a pedagogical aim, it begins with an introductory chapter devoted to multivectors and Clifford algebra for the three-dimensional space. In a later chapter modifications are presented necessary for higher dimension and for the pseudoeuclidean metric of the Minkowski space.Among other advantages one is worth mentioning: Due to a bivectorial description of the magnetic field a notion of force surfaces naturally emerges, which reveals an intimate link between the magnetic field and the electric currents as its sources. Because of the elementary level of presentation, this book can be treated as an introductory course to electromagnetic theory. Numerous illustrations are helpful in visualizing the exposition. Furthermore, each chapter ends with a list of problems which amplify or further illustrate the fundamental arguments. |
Содержание
Preface | 1 |
Nabla Operator | 46 |
Clifforvalued Distributions | 56 |
ELECTROMAGNETIC FIELD | 69 |
Other Examples of Static Magnetic Fields | 99 |
Simplest NonStatic Electromagnetic Fields | 107 |
ELECTROMAGNETIC POTENTIALS | 114 |
Multipole Expansion | 132 |
CHARGES IN THE ELECTROMAGNETIC FIELD | 151 |
PLANE ELECTROMAGNETIC FIELDS | 172 |
VARIOUS KINDS OF ELECTROMAGNETIC | 206 |
SPECIAL RELATIVITY | 227 |
RELATIVITY AND ELECTRODYNAMICS | 274 |
Charge in the Electromagnetic Field | 295 |
BEHAVIOUR OF THE INTEGRAL 1 33 | 305 |
315 | |
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Часто встречающиеся слова и выражения
a₁ angle anticommutes arbitrary axis b₁ bivector boundary called charge Clifford algebra Clifford product commutes component conductor constant coordinates corresponding cosh covariant denoted density depend derivative differential dipole direction e₁ electric field electromagnetic field energy equal expression factors force surfaces formula function harmonic wave hence Hodge map identity implies inner product integral introduce Lemma linear space Lorentz condition Lorentz transformations magnetic field magnitude Maxwell equation Minkowski space motion multivectors nonzero obtain orientation orthogonal outer product parallel particle perpendicular plates polarization Poynting vector Problem product of vectors pseudovectors quadrivector quantities r₁ right-hand side rotation satisfied scalar product shown in Fig sinh solution space-like space-time superposition symmetry term three-dimensional space time-like trivector uniform unit vector vector potential velocity virtue volutor write zero
Популярные отрывки
Стр. 316 - Quaternionic formulation of classical electrodynamics and theory of functions of a biquaternion variable, Report of Fundamental Physics Laboratory, Department of Electronic Science, Faculty of Science, Okayama University of Science, Feb.
Стр. 315 - M. Riesz, Clifford Numbers and Spinors , Lecture Series No. 38 (University of Maryland, College Park, 1958), Chaps.
Стр. 315 - Thome and John Archibald Wheeler, "Gravitation" (Freeman and Co., San Francisco, 1973). 2. Walter Thirring, "Course in Mathematical Physics", vol. 2: "Classical Field Theory" (Springer Verlag, Vienna, 1982).