proposition 14.60 The quadratic invariant
open in the book ·
parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2751
· p. 573
Rests on
-
depends_on
definition 14.8
Casimir element
¶
-
depends_on
definition 14.5
Universal enveloping algebra
¶
-
depends_on
equation 14.5
eq:lie-structconst
¶
-
step_from
equation 14.4
eq:lie-gengrlie
¶
- step_from equation 14.3 eq:lie-generators ¶
- step_from equation 14.2 eq:lie-varincor ¶
-
step_from
equation 14.4
eq:lie-gengrlie
¶
-
depends_on
equation 14.5
eq:lie-structconst
¶
-
depends_on
definition 14.5
Universal enveloping algebra
¶
- depends_on equation 14.97 eq:lie-jp-comm ¶
- depends_on equation 14.84 eq:lie-transl-comm ¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-28 ¶
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 |
→ | Casimir element | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2754 |
depends_on |
→ | eq:lie-jp-comm | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2754 |
depends_on |
→ | eq:lie-transl-comm | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2754 |
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-28 | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2757 |