lemma A.386 The little group

open in the book · appendices/A-long-proofs.tex:18870 · p. 2980

Rests on

depends_on definition A.384 The mass shell and the standard momentum ¶
- depends_on lemma 14.68 The algebra fixing a timelike momentum ¶
  - depends_on equation 14.23 eq:lie-sopq-defining ¶
  - depends_on proposition 14.22 The rank of $\mathfrak{so}(p,q)$ ¶
    - depends_on definition 14.20 Cartan subalgebra and rank ¶
    - depends_on equation 14.90 eq:lie-algebrasopq ¶
    - depends_on theorem 14.21 Racah ¶
      - depends_on definition 14.8 Casimir element ¶
      - depends_on definition 14.20 Cartan subalgebra and rank ¶ ↺
      - proves proof ch:12-lie-groups-fibre-bundles@prooflink-3 ¶
    - proves proof ch:12-lie-groups-fibre-bundles@proof-7 ¶
  - proves proof ch:12-lie-groups-fibre-bundles@proof-32 ¶
- depends_on notation 14.1 not:lie-indices ¶
depends_on equation 14.23 eq:lie-sopq-defining ¶ ↺
depends_on lemma 14.68 The algebra fixing a timelike momentum ¶ ↺
proves proof app:A-long-proofs@proof-233 ¶

Supports

depends_on proposition A.390 Construction ¶
- depends_on proposition A.391 Reducible little-group data give reducible representations ¶
- depends_on theorem A.392 Wigner–Mackey classification; quoted ¶

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`	→	The mass shell and the standard momentum	declared	appendices/A-long-proofs.tex:18874
`depends_on`	→	eq:lie-sopq-defining	declared	appendices/A-long-proofs.tex:18874
`depends_on`	→	The algebra fixing a timelike momentum	declared	appendices/A-long-proofs.tex:18874
`depends_on`	←	Construction	declared	appendices/A-long-proofs.tex:19058
`proves`	←	app:A-long-proofs@proof-233	declared	appendices/A-long-proofs.tex:18877