example 24.52 The prequantum line and the Schrödinger representation

open in the book · parts/03-classical-mechanics/07-symplectic-geometry.tex:1781 · p. 869

example -- no derivation owed by its kind

Rests on

depends_on equation 24.6 eq:sym-hamiltonian-field-coords ¶
depends_on proposition 24.51 Prequantization is a Lie-algebra homomorphism ¶
- depends_on definition 24.50 Prequantum operator ¶
  - depends_on definition 24.14 Hamiltonian vector field ¶
    - depends_on definition 24.8 Symplectic manifold ¶
      - depends_on definition 13.105 Closed form ¶
      - depends_on definition 13.98 $k$-form ¶
      - depends_on definition 24.2 Symplectic vector space ¶
    - 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 definition 14.103 Connection $1$-form ¶
      - depends_on definition 14.97 Principal 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 equation 24.8 eq:sym-bracket-homomorphism ¶
- depends_on equation 24.34 eq:sym-prequantum-condition ¶
- proves proof ch:07-symplectic-geometry@proof-16 ¶

Supports

Nothing declares a dependency on this node yet.

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:sym-hamiltonian-field-coords	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1803
`depends_on`	→	Prequantization is a Lie-algebra homomorphism	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1803