Electrodynamics: A Modern Geometric Approach
The emphasis in this text is on classical electromagnetic theory and electrodynamics, that is, dynamical solutions to the Lorentz-force and Maxwell's equations. The natural appearance of the Minkowski spacetime metric in the paravector space of Clifford's geometric algebra is used to formulate a covariant treatment in special relativity that seamlessly connects spacetime concepts to the spatial vector treatments common in undergraduate texts. Baylis' geometrical interpretation, using such powerful tools as spinors and projectors, essentially allows a component-free notation and avoids the clutter of indices required in tensorial treatments. The exposition is clear and progresses systematically - from a discussion of electromagnetic units and an explanation of how the SI system can be readily converted to the Gaussian or natural Heaviside-Lorentz systems, to an introduction of geometric algebra and the paravector model of spacetime, and finally, special relativity. Other topics include Maxwell's equation(s), the Lorentz-force law, the Fresnel equations, electromagnetic waves and polarization, wave guides, radiation from accelerating charges and time-dependent currents, the Liénard-Wiechert potentials, and radiation reaction, all of which benefit from the modern relativistic approach. Numerous worked examples and exercises dispersed throughout the text help the reader understand new concepts and facilitate self-study of the material. Each chapter concludes with a set of problems, many with answers. Complete solutions are also available. An excellent feature is the integration of Maple into the text, thereby facilitating difficult calculations. To download accompanying Maple worksheets, please visit http://www.cs.uwindsor.ca/users/b/baylis
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angle anticommutes approach basis elements basis vectors bivector canonical element chapter charge Clifford algebras Clifford's geometric algebra collinear commute complex numbers components coordinate covariant cross product defined differential forms dimensional Dirac eie2 plane electric electrodynamics electromagnetic field electromagnetic theory electromagnetic units energy equations Euclidean space example Exercise expressed factors Gaussian system Gaussian units geometric algebra grades Hamilton's quaternions hermitian conjugation Hodge dual inertial frame inverse involution linear space Lorentz transformations m-vector subspace magnetic mathematical matrix representation Maxwell's metric tensor Minkowski spacetime n-dimensional notation orthonormal paravector paravector space particle Pauli algebra perpendicular physicists physics problem projector real paravectors real scalar relation relativistic relativity represent rotation scalar and vector spacetime momentum spacetime plane spacetime vector spatial reversal spatial vectors speed of light square length statcoul statcoulomb statvolt three dimensions trivector unimodular unit bivector eie2 unit systems unit vectors vector algebra vector product vector space volume element whereas