The Wigner–Eckart Theorem and Other Applications

Nadir Jeevanjee ()
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Nadir Jeevanjee: University of California, Department of Physics

Chapter Chapter 6 in An Introduction to Tensors and Group Theory for Physicists, 2011, pp 213-226 from Springer

Abstract: Abstract Chapter 6 applies the material of the previous chapters to some particular topics, specifically the Wigner–Eckart theorem, selection rules, and gamma matrices and Dirac bilinears. We begin by discussing the perennially confusing concepts of vector operators and spherical tensors, and then unify them using the notion of a representation operator. We then use this framework to derive a generalized selection rule, from which the various quantum-mechanical selection rules can be derived, and we also discuss the Wigner–Eckart theorem. We conclude by showing that Dirac’s famous gamma matrices can be understood in terms of representation operators, which then immediately gives the transformation properties of the ‘Dirac bilinears’ of QED.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4715-5_6

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DOI: 10.1007/978-0-8176-4715-5_6

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