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arXiv · 1509.05633

Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group

Giuseppe Sellaroli
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Abstract

The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. This paper generalises it to arbitrary Lie groups, possibly non-compact. The result relies on knowledge of recoupling theory between finite-dimensional and arbitrary admissible representations, which may be infinite-dimensional; the particular case of the Lorentz group will be studied in detail. As an application, the Wigner-Eckart theorem will be used to construct an analogue of the Jordan-Schwinger representation, previously known only for finite-dimensional representations of the Lorentz group, valid for infinite-dimensional ones.

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Giuseppe Sellaroli. 2015-09-18. Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group. https://arxiv.org/abs/1509.05633

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