definition 14.97 Principal bundle

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4117 · p. 588

ground object -- no derivation owed

Rests on

depends_on definition 14.95 Fibre bundle ¶

Supports

depends_on definition 14.99 Associated bundle ¶
depends_on definition 14.103 Connection $1$-form ¶
- depends_on definition 14.105 Curvature $2$-form ¶
  - depends_on definition 24.49 Prequantum datum ¶
    - depends_on definition 24.53 Real polarization and polarized sections ¶
      - depends_on proposition 24.54 The vertical polarization gives wave mechanics ¶
    - depends_on definition 24.50 Prequantum operator ¶
      - depends_on proposition 24.51 Prequantization is a Lie-algebra homomorphism ¶
      - depends_on proposition 24.54 The vertical polarization gives wave mechanics ¶ ↺
    - depends_on proposition 24.56 The Bohr–Sommerfeld condition is a triviality condition on the prequantum holonomy ¶
      - depends_on remark 24.57 The half-integer, and the honest status of the construction ¶
  - depends_on proposition 14.106 The curvature is horizontal, and measures non-integrability ¶
    - depends_on proposition 14.114 Chern–Weil forms descend to the base ¶
      - depends_on definition 14.115 Characteristic forms ¶
  - depends_on theorem 14.107 Bianchi identity ¶
- depends_on definition 24.49 Prequantum datum ¶ ↺
- depends_on proposition 14.104 A connection splits the tangent space ¶
  - depends_on proposition 14.106 The curvature is horizontal, and measures non-integrability ¶ ↺
depends_on proposition 14.98 A principal bundle is trivial if and only if it has a global section ¶

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`	→	Fibre bundle	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4130
`depends_on`	←	Associated bundle	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4172
`depends_on`	←	Connection $1$-form	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4277
`depends_on`	←	A principal bundle is trivial if and only if it has a global section	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4136