Birdtracks for SU(N)

Abstract

I gently introduce the diagrammatic birdtrack notation, first for vector algebra and then for permutations. After moving on to general tensors I review some recent results on Hermitian Young operators, gluon projectors, and multiplet bases for SU(N) color space.

Lecture notes for the QCD Master Class 2017, https://indico.cern.ch/event/547800/, 18-24 June 2017, Saint-Jacut-de-la-Mer, France; introduction added, minor corrections

References in corpus (4)

• ColorMath - A package for color summed calculations in SU(Nc)
• Compact Hermitian Young Projection Operators
• Transition Operators
• Simplification Rules for Birdtrack Operators

Cited by in corpus (10)

• Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ansätze
• Systematic construction of basis invariants in the 2HDM
• Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry
• 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
• Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections
• Constraining the Higgs Trilinear Coupling from an $SU(2)$ Quadruplet with Bounded-from-Below Conditions
• Next-to-Leading Order QCD Corrections to Heavy-Flavour Production in Neutral Current DIS
• Towards Symmetry-Aware Efficient Simulation of Quantum Systems and Beyond
• On currents in the $O(n)$ loop model