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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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SPACE AND TIME PROPERTIES

SPACE AND TIME PROPERTIES

Chapter:
(p.59) 3 SPACE AND TIME PROPERTIES
Source:
Multipole Theory in Electromagnetism
Author(s):

R. E. Raab

O. L. de Lange

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567271.003.0003

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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