lemma 14.64 Properties of $W$
open in the book ·
parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2850
· p. 574
Rests on
-
depends_on
definition 14.63
Pauli–Lubanski vector
¶
- depends_on equation 14.86 eq:lie-sopq-gen ¶
- depends_on equation 14.82 eq:lie-transl-gen ¶
- depends_on equation 14.90 eq:lie-algebrasopq ¶
- depends_on equation 14.97 eq:lie-jp-comm ¶
- depends_on equation 14.84 eq:lie-transl-comm ¶
-
depends_on
lemma 14.62
The Levi-Civita symbol is invariant
¶
- depends_on equation 13.223 eq:mfd-epsilon-density ¶
-
depends_on
example 13.94
The two densities this chapter uses
¶
-
depends_on
definition 13.92
Tensor density
¶
-
depends_on
definition 13.89
Contravariant and covariant tensors
¶
- depends_on definition 13.88 General coordinate transformation ¶
- depends_on definition 13.88 General coordinate transformation ¶ ↺
-
depends_on
definition 13.89
Contravariant and covariant tensors
¶
-
depends_on
proposition 13.93
Algebra of densities
¶
- depends_on definition 13.92 Tensor density ¶ ↺
- proves proof ch:11-manifolds-tensors-curvature@proof-17 ¶
-
depends_on
definition 13.92
Tensor density
¶
- depends_on notation 14.1 not:lie-indices ¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-29 ¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-30 ¶
Supports
- depends_on theorem 14.65 The two Casimir operators of the Poincaré algebra in $3+1$ dimensions ¶
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 |
→ | Pauli–Lubanski vector | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2857 |
depends_on |
→ | eq:lie-algebrasopq | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2857 |
depends_on |
→ | eq:lie-jp-comm | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2857 |
depends_on |
→ | eq:lie-transl-comm | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2857 |
depends_on |
→ | The Levi-Civita symbol is invariant | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2857 |
depends_on |
← | The two Casimir operators of the Poincaré algebra in $3+1$ dimensions | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2903 |
proves |
← | ch:12-lie-groups-fibre-bundles@proof-30 | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2860 |