definition 14.103 Connection $1$-form

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4258 · p. 590

ground object -- no derivation owed

Rests on

depends_on definition 14.97 Principal bundle ¶
- depends_on definition 14.95 Fibre bundle ¶
depends_on notation 14.101 Algebra-valued forms and their bracket ¶

Supports

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 remark 24.55 What polarization costs ¶
  - depends_on definition 24.50 Prequantum operator ¶
    - depends_on proposition 24.51 Prequantization is a Lie-algebra homomorphism ¶
      - depends_on example 24.52 The prequantum line and the Schrödinger representation ¶
    - 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 ¶ ↺

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`	→	Principal bundle	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4277
`depends_on`	→	Algebra-valued forms and their bracket	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4277
`depends_on`	←	Curvature $2$-form	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4313
`depends_on`	←	Prequantum datum	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1701
`depends_on`	←	A connection splits the tangent space	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4285