Abstract
Electronic and vibrational states of crystals are classified according to the IRs of space groups. Thus, as a first step we have to establish these IRs, which is done in this chapter for the ordinary as well as the magnetic and double space groups. In any case the basic group to be discussed is the little group. Its IRs can be obtained from the projective REPs as well as from ordinary vector REPs. The discussion of the magnetic space groups needs the CORs. In addition, the projection operators for the construction of the symmetry adapted basis functions are given.
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References
H.-W. Streitwolf: Gruppentheorie in der Festkörperphysik (Akademische Verlagsgesellschaft, Leipzig 1967)
A.P. Cracknell: Group Theory in Solid-State Physics (Taylor & Francis, London 1975)
W. Döring: Die Strahldarstellungen der kristallographischen Gruppen. Z. Naturforsch. 14a, 343 (1959)
W. Döring, V. Zehler: Gruppentheoretische Untersuchung der Elektronenbänder im Diamantgitter. Ann. Phys. (Leipzig) (6) 13, 214 (1953)
O.V. Kovalev: Irreducible Representations of the Space Groups (Gordon and Breach, New York 1965)
G.L. Bir, G.E. Pinkus: Symmetry and Strain-Induced Effects in Semiconductors (Wiley, New York 1974)
J. Zak (ed.): The Irreducible Respresentations of Space Groups (Benjamin, Elmsford, NY 1969)
G.J. Bradley, A.P. Cracknell: The Mathematical Theory of Symmetry in Solids (Clarendon, Oxford 1972)
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© 1996 Springer-Verlag Berlin Heidelberg
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Ludwig, W., Falter, C. (1996). Representations of Space Groups. In: Symmetries in Physics. Springer Series in Solid-State Sciences, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79977-8_9
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DOI: https://doi.org/10.1007/978-3-642-79977-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60284-2
Online ISBN: 978-3-642-79977-8
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