Spherical Harmonics and Tensors for Classical Field Theory (Electronic and Electrical Engineering Research Studies Applied and Engineering Mathematic) - Softcover

Jones, M. N.

9780471907664: Spherical Harmonics and Tensors for Classical Field Theory (Electronic and Electrical Engineering Research Studies Applied and Engineering Mathematic)

Softcover

ISBN 10: 0471907669 ISBN 13: 9780471907664

Publisher: John Wiley & Sons Inc, 1985

Presents the theory of spherical harmonics in a form suitable for the analysis of non-separable, nonlinear, partial differential equations, defined in a spherical or infinite domain. Describes and develops those aspects of group theory that are relevant to classical field theory. Each harmonic is labeled by a particular irreducible representation of the three-dimensional rotation group. Shows how to apply tensor harmonic techniques to all branches of classical field theory, including fluid mechanics, electromagnetism, geophysics and the atmospheric sciences.

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Synopsis:

Classical applied mathematics and theoretical physics owe much to the influence of quantum mechanics in the development and application of a wide range of theoretical techniques. It is only relatively recently that group theory, which has always played a fundamental role in quantum theory, has been applied to problems in classical field theory. This book describes and develops those aspects of group theory which are especially relevant to classical field theory, with particular reference to systems with spherical symmetry. In order to establish a perspective, a specific partial differential equation of fluid mechanics, well known in meteorology, is considered in detail, using traditional methods. The elements of formal group theory are then presented in Chapter 2. The rotation group, which plays a fundamental role in the present approach, is considered in Chapter 3. In Chapter 4, the theory is extended to permit the tensor spherical harmonic to be defined.

The remaining chapters consider specific techniques, for example multipole moments and Green functions, which are relevant to all branches of classical field theory, including fluid mechanics, electromagnetism, geophysics and the atmospheric sciences. Applications of the theory to some of these areas are considered in the final chapters.

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