proposition 14.52 Structure constants and the symmetric tensor

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1984 · p. 564

Rests on

depends_on definition 14.51 Gell-Mann basis ¶
- depends_on definition 14.49 The special unitary group in three dimensions ¶
proves proof ch:12-lie-groups-fibre-bundles@proof-22 ¶
proves proof ch:12-lie-groups-fibre-bundles@prooflink-5 ¶

Supports

depends_on proposition 14.54 The two Casimir operators of $\mathfrak{su}(3)$ ¶
- depends_on example A.358 Rank two: $\mathfrak{su}(3)$ ¶
depends_on proposition 14.53 Killing form of $\mathfrak{su}(3)$ ¶
- depends_on proposition 14.55 The fundamental, the antifundamental and the adjoint ¶
  - depends_on corollary A.377 The adjoint representation is irreducible ¶
  - depends_on example A.358 Rank two: $\mathfrak{su}(3)$ ¶ ↺
  - depends_on theorem 14.57 $\vect{3}\otimes\bar{\vect{3}} = \vect{1}\oplus\vect{8}$ ¶
    - depends_on proposition 102.6 Mesons are $q\bar{q}$, baryons are $qqq$ ¶
      - assumes experiment Deep Inelastic Scattering ¶
      - depends_on phenomenon 116.38 The quark spins do not account for the proton spin ¶
      - depends_on phenomenon 102.9 The $\Delta^{++}$ violates the spin-statistics theorem ¶
      - depends_on phenomenon 102.7 The nucleon magnetic moments come out right ¶
      - depends_on proposition 116.29 The Gross–Llewellyn Smith sum rule in the parton model ¶
  - depends_on theorem 102.12 Which quark combinations can be colour singlets ¶
    - depends_on corollary 102.13 The selection rule of the eightfold way ¶
- depends_on proposition 14.54 The two Casimir operators of $\mathfrak{su}(3)$ ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Gell-Mann basis	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2014
`depends_on`	←	The two Casimir operators of $\mathfrak{su}(3)$	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2182
`depends_on`	←	Killing form of $\mathfrak{su}(3)$	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2073
`proves`	←	ch:12-lie-groups-fibre-bundles@proof-22	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2017
`proves`	←	ch:12-lie-groups-fibre-bundles@prooflink-5	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2061