theorem 14.111 Chern–Weil
open in the book ·
parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4670
· p. 594
Rests on
- depends_on equation 14.142 eq:lie-bianchi ¶
- depends_on equation 14.139 eq:lie-curvature ¶
-
depends_on
theorem 14.110
thm:lie-invpoly
¶
-
depends_on
definition 14.109
$G$-invariant polynomial
¶
- depends_on equation 14.144 eq:lie-invpol-linear ¶
- depends_on equation 14.145 eq:lie-invpol-symm ¶
-
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
¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-45 ¶
-
depends_on
definition 14.109
$G$-invariant polynomial
¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-46 ¶
Supports
- depends_on definition 14.115 Characteristic forms ¶
-
depends_on
definition 14.112
Chern–Simons form
¶
-
depends_on
proposition 14.113
The Chern–Simons forms of degree $3$ and $5$
¶
- depends_on proposition 14.117 The quadratic invariant and its Chern–Simons form ¶
-
depends_on
proposition 14.113
The Chern–Simons forms of degree $3$ and $5$
¶
-
depends_on
proposition 14.114
Chern–Weil forms descend to the base
¶
- depends_on definition 14.115 Characteristic forms ¶ ↺
-
depends_on
proposition 106.81
The topological charge is an integer
¶
- depends_on proposition 106.83 The vacuum is a superposition of winding sectors ¶
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 |
→ | eq:lie-bianchi | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4708 |
depends_on |
→ | eq:lie-curvature | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4708 |
depends_on |
→ | thm:lie-invpoly | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4708 |
depends_on |
← | Characteristic forms | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5125 |
depends_on |
← | Chern–Simons form | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4924 |
depends_on |
← | Chern–Weil forms descend to the base | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5065 |
depends_on |
← | The topological charge is an integer | declared | parts/11-qft-standard-model/08-path-integral-quantization.tex:3833 |
proves |
← | ch:12-lie-groups-fibre-bundles@proof-46 | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4711 |