Transition Operators

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.

arXiv comment44 pages. Description of limitations on direct application of Young projectors included. This has no impact on the main results

References in corpus (4)

• Orthogonal multiplet bases in SU(Nc) color space
• Hermitian Young Operators
• Compact Hermitian Young Projection Operators
• Simplification Rules for Birdtrack Operators

Cited by in corpus (11)

• Systematic construction of basis invariants in the 2HDM
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Compact Hermitian Young Projection Operators
• Birdtracks for SU(N)
• QCD multiplet bases with arbitrary parton ordering
• Simplification Rules for Birdtrack Operators
• Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
• The chirality-flow formalism
• Wigner 6j symbols for SU(N): Symbols with at least two quark-lines
• Wigner 6j symbols with gluon lines: completing the set of 6j symbols required for color decomposition
• A simple counting argument of the irreducible representations of SU(N) on mixed product spaces