equation 14.15 eq:lie-killing-components

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Supports

• depends_on lemma 14.41 Ladder algebra ¶
  • depends_on proposition 14.44 Existence: every allowed $j$ is realized ¶
    • depends_on proposition 14.45 Which representations descend to $\SO(3,\R)$ ¶
  • depends_on theorem 14.43 The irreducible representations of $\mathfrak{su}(2)$ ¶
    • depends_on example A.394 $D = 4$ ¶
    • depends_on example A.357 Rank one: $\mathfrak{su}(2)$ ¶
    • depends_on proposition 14.44 Existence: every allowed $j$ is realized ¶ ↺
    • depends_on theorem 14.47 Clebsch–Gordan series ¶
• 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 $\mathfrak{su}(3)$ ¶
    • depends_on example A.358 Rank two: $\mathfrak{su}(3)$ ¶ ↺