theorem 14.21 Racah

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:636 · p. 548

Rests on

depends_on proposition 14.22 The rank of $\mathfrak{so}(p,q)$ ¶
- depends_on lemma 14.68 The algebra fixing a timelike momentum ¶
  - depends_on definition A.384 The mass shell and the standard momentum ¶
    - depends_on lemma A.387 Standard boost and transitivity ¶
      - depends_on lemma A.388 The invariant measure ¶
      - depends_on proposition A.390 Construction ¶
    - depends_on lemma A.386 The little group ¶
      - depends_on proposition A.390 Construction ¶ ↺
    - depends_on lemma A.388 The invariant measure ¶ ↺
    - depends_on theorem A.385 Labels of a massive representation ¶
      - depends_on example A.394 $D = 4$ ¶
    - depends_on theorem A.392 Wigner–Mackey classification; quoted ¶
  - depends_on lemma A.386 The little group ¶ ↺
  - depends_on theorem A.385 Labels of a massive representation ¶ ↺
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 theorem A.385 Labels of a massive representation ¶ ↺

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Casimir element	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:642
`depends_on`	→	Cartan subalgebra and rank	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:642
`depends_on`	←	The rank of $\mathfrak{so}(p,q)$	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:675
`depends_on`	←	The two Casimir operators of $\mathfrak{su}(3)$	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2182
`depends_on`	←	Labels of a massive representation	declared	appendices/A-long-proofs.tex:18860
`proves`	←	ch:12-lie-groups-fibre-bundles@prooflink-3	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:652