definition 14.109 $G$-invariant polynomial
open in the book ·
parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4463
· p. 592
- ground object -- no derivation owed
Rests on
- depends_on equation 14.144 eq:lie-invpol-linear ¶
- depends_on equation 14.145 eq:lie-invpol-symm ¶
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 lemma 14.116 Invariance of the characteristic coefficients ¶
-
depends_on
proposition 14.114
Chern–Weil forms descend to the base
¶
- depends_on definition 14.115 Characteristic forms ¶ ↺
- 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
theorem 14.110
thm:lie-invpoly
¶
-
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 14.111
Chern–Weil
¶
- depends_on definition 14.115 Characteristic forms ¶ ↺
- depends_on definition 14.112 Chern–Simons form ¶ ↺
- depends_on proposition 14.114 Chern–Weil forms descend to the base ¶ ↺
-
depends_on
proposition 106.81
The topological charge is an integer
¶
- depends_on proposition 106.83 The vacuum is a superposition of winding sectors ¶
-
depends_on
proposition 14.54
The two Casimir operators of $\mathfrak{su}(3)$
¶
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-invpol-linear | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4479 |
depends_on |
→ | eq:lie-invpol-symm | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4479 |
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 |
← | Invariance of the characteristic coefficients | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5139 |
depends_on |
← | Chern–Weil forms descend to the base | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5065 |
depends_on |
← | The Chern–Simons forms of degree $3$ and $5$ | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5006 |
depends_on |
← | The quadratic invariant and its Chern–Simons form | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5194 |
depends_on |
← | thm:lie-invpoly | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4529 |