proposition 25.4 Leibniz rule and derivations

open in the book · parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:171 · p. 874

Rests on

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 13.103 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 equation 22.4 eq:ham-pdot ¶
- depends_on equation 22.3 eq:ham-qdot ¶
depends_on theorem 25.3 The bracket is a Lie bracket ¶
- depends_on equation 22.41 eq:ham-poisson-bracket ¶
- depends_on equation 22.56 eq:ham-symplectic-matrix ¶
- proves proof ch:08-poisson-quantum-bridge@proof-1 ¶
proves proof ch:08-poisson-quantum-bridge@proof-2 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Hamiltonian vector field	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:178
`depends_on`	→	The bracket is a Lie bracket	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:178
`depends_on`	←	The four identities	declared	appendices/A-long-proofs.tex:29637
`proves`	←	ch:08-poisson-quantum-bridge@proof-2	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:181