proposition 24.54 The vertical polarization gives wave mechanics

open in the book · parts/03-classical-mechanics/07-symplectic-geometry.tex:1818 · p. 869

Rests on

depends_on definition 24.53 Real polarization and polarized sections ¶
- depends_on definition 24.8 Symplectic manifold ¶
  - depends_on definition 13.105 Closed form ¶
    - depends_on definition 13.103 Exterior derivative ¶
      - depends_on definition 13.98 $k$-form ¶
      - depends_on definition 13.102 Wedge product ¶
    - depends_on definition 13.98 $k$-form ¶ ↺
  - depends_on definition 13.98 $k$-form ¶ ↺
  - depends_on definition 24.2 Symplectic vector space ¶
    - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
      - depends_on definition 5.110 Bilinear map ¶
      - depends_on definition 5.113 Non-degenerate form ¶
      - depends_on definition 5.111 Symmetric and antisymmetric forms ¶
      - depends_on equation 5.139 eq:lin-bilinear-congruence ¶
      - proves proof ch:03-linear-algebra-representations@proof-54 ¶
- depends_on definition 24.49 Prequantum datum ¶
  - depends_on definition 14.103 Connection $1$-form ¶
    - 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 ¶
  - depends_on definition 14.105 Curvature $2$-form ¶
    - depends_on definition 14.103 Connection $1$-form ¶ ↺
    - depends_on notation 14.101 Algebra-valued forms and their bracket ¶ ↺
  - depends_on definition 24.8 Symplectic manifold ¶ ↺
depends_on definition 24.50 Prequantum operator ¶
- depends_on definition 24.14 Hamiltonian vector field ¶
  - depends_on definition 24.8 Symplectic manifold ¶ ↺
  - depends_on equation 22.4 eq:ham-pdot ¶
  - depends_on equation 22.3 eq:ham-qdot ¶
- depends_on definition 24.49 Prequantum datum ¶ ↺
depends_on equation 24.35 eq:sym-prequantum-local ¶
proves proof ch:07-symplectic-geometry@proof-17 ¶

Supports

depends_on remark 24.55 What polarization costs ¶

Neighborhood

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Edges

type	direction	node	provenance	where
`depends_on`	→	Real polarization and polarized sections	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1830
`depends_on`	→	Prequantum operator	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1830
`depends_on`	→	eq:sym-prequantum-local	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1830
`depends_on`	←	What polarization costs	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1881
`proves`	←	ch:07-symplectic-geometry@proof-17	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1834