Discrete and Continuous Symmetry via Induction and Duality

Peter Kramer and Miguel Lorente
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Peter Kramer: Universität Tübingen, Institut für Theoretische Physik
Miguel Lorente: Universidad de Oviedo, Departamento de Física

A chapter in Symmetries in Science X, 1998, pp 165-177 from Springer

Abstract: Abstract We study the relation of discrete versus continuous symmetry by use of induc-tion/subduction techniques and duality of Abelian groups. We start with translations, then move on to point transformations and to the Euclidean and Non-Euclidean semidi-rect product groups and their representations. The UIR of discrete space groups are characterized by functions on the dual translation groups which correspond to difference equations on the lattice.

Keywords: Difference Equation; Brillouin Zone; Fundamental Domain; Dual Group; Translation Group (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-1537-5_10

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DOI: 10.1007/978-1-4899-1537-5_10

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