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arXiv · 1610.08802

Transition Operators

Judith Alcock-Zeilinger·Heribert Weigert
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Abstract

In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of SU(N), using the compact expressions of Hermitian Young projection operators derived in a companion paper. We show that the Hermitian Young projection operators together with their transition operators constitute a fully orthogonal basis for the algebra of invariants of $V^{\otimes m}$ that exhibits a systematically simplified multiplication table. We discuss the full algebra of invariants over $V^{\otimes 3}$ and $V^{\otimes 4}$ as explicit examples. In our presentation we make use of various standard concepts such as Young projection operators, Clebsch-Gordan operators, and invariants (in birdtrack notation). We tie these perspectives together and use them to shed light on each other.

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Judith Alcock-Zeilinger, Heribert Weigert. 2016-10-27. Transition Operators. https://doi.org/10.1063/1.4983479

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