Multivectors and Clifford Algebra in Electrodynamics
World 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.
Отзывы - Написать отзыв
Не удалось найти ни одного отзыва.
CHARGES IN THE ELECTROMAGNETIC FIELD 1 Motion of a Charge in a Uniform Field 2 System of Charges in an External Field 3 Lagrange a...
Examples of Electromagnetic Fields and Potentials 2 1 The Uniform Field 2 2 Field of the Electric Charge 2 3 Field of the Linear Current 2 4 The Pla...
Charge in the Electromagnetic Field
BEHAVIOUR OF THE INTEGRAL 1 33
Другие издания - Просмотреть все
angle anticommutes antisymmetric arbitrary axis bivector boost boundary called charge Q Clifford algebra Clifford product coefficient commutes component conductor consider constant coordinates corresponding cosh covariant curve defined denoted depend derivative differential dipole direction electric field electromagnetic cliffor electromagnetic field energy energy-momentum cliffor equal expression factors force surfaces formula function hence Hodge map identity implies inner product integral introduce Lemma linear space Lorentz condition Lorentz transformations magnetic field magnetic induction magnitude Maxwell equation means Minkowski space momentum motion multivector nonzero obtain opposite orientation orthogonal outer product parallel particle perpendicular plates polarization Poynting vector Problem product of vectors pseudovectors quadrivector quantities region right-hand side rotation satisfied scalar product shown in Fig sinh solenoid solution space-like space-time superposition surface currents symmetry tensor term three-dimensional space time-like trivector uniform unit vector vector potential velocity virtue volutor write zero