Simplification Rules for Birdtrack Operators

Abstract

This paper derives a set of easy-to-use tools designed to simplify calculations with birdtrack op- erators comprised of symmetrizers and antisymmetrizers. In particular, we present cancellation rules allowing one to shorten the birdtrack expressions of operators, and propagation rules identifying the circumstances under which it is possible to propagate symmetrizers past antisymmetrizers and vice versa. We exhibit the power of these simplification rules by means of a short example in which we apply the tools derived in this paper on a typical operator that can be encountered in the representation theory of SU(N) over the product space $V^{\otimes m}$ . These rules form the basis for the construction of compact Hermitian Young projection operators and their transition operators addressed in companion papers.

arXiv comment33 pages, proof of theorem 3 expanded

References in corpus (9)

• The Construction of Gauge-Links in Arbitrary Hard Processes
• Non-global jet evolution at finite N_c
• New observables to test the Color Glass Condensate beyond the large-N_c limit
• Orthogonal multiplet bases in SU(Nc) color space
• JIMWLK evolution of the odderon
• Multiple Gluon Exchange Webs
• Hermitian Young Operators
• Compact Hermitian Young Projection Operators
• Transition Operators

Cited by in corpus (7)

• Systematic construction of basis invariants in the 2HDM
• Compact Hermitian Young Projection Operators
• Transition Operators
• Birdtracks for SU(N)
• 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