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Multipole Theory in ElectromagnetismClassical, quantum, and symmetry aspects, with applications$
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Roger E. Raab and Owen L. de Lange

Print publication date: 2004

Print ISBN-13: 9780198567271

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198567271.001.0001

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Multipole Theory in Electromagnetism

R. E. Raab

O. L. de Lange

Oxford University Press

Polar and axial vectors and tensors are defined in terms of their behaviour under coordinate transformations. The effect of the time-reversal operator on kets and matrix elements is considered, followed by a tabulation of the space and time properties of various tensors — mechanical, electromagnetic, isotropic, and multipole. An account is given of the point-group symmetries of molecules and non-magnetic and magnetic crystals, with worked examples of the effect of symmetry on the components of a property tensor. The origin dependence of multipole moment operators is derived and used to obtain that of polarizability tensors up to electric octopole-magnetic quadrupole order. A pictorial approach is described for determining the symmetry conditions for the existence of an equilibrium effect and this is illustrated for the Faraday effect in a fluid and crystal.

Keywords:   tensor definitions, time-reversal operator, space-time tensor properties, molecular point groups, crystalline point groups, magnetic crystals, origin dependences, pictorial analysis of symmetry conditions, Kerr effect

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