definition 25.6 Infinitesimal canonical transformation

open in the book · parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:250 · p. 875

ground object -- no derivation owed

Rests on

depends_on definition 22.29 Poisson bracket ¶
- depends_on definition 7.97 Partial derivative; gradient ¶
  - depends_on definition 7.26 Derivative of a function at a point ¶
    - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 7.9 Real function ¶ ↺
  - depends_on definition 5.15 Basis ¶
    - depends_on definition 5.12 Subspace generated by a set of vectors ¶
      - depends_on definition 5.5 Linear combination ¶
      - depends_on definition 5.7 Vector subspace ¶
      - proves proof ch:03-linear-algebra-representations@proof-3 ¶
    - depends_on definition 5.14 Linear independence ¶
      - depends_on definition 5.5 Linear combination ¶ ↺
- depends_on definition 22.14 Phase-space coordinate transformation ¶
  - depends_on definition 22.2 Hamiltonian ¶
    - depends_on definition 21.34 Generalized momentum ¶
    - depends_on definition 21.31 Lagrangian ¶
depends_on definition 24.17 Symplectomorphism ¶
- depends_on definition A.70 Pullback ¶
  - depends_on definition 7.97 Partial derivative; gradient ¶ ↺
  - depends_on definition 13.83 Covector ¶
    - depends_on definition 13.81 Vector on a manifold ¶
      - depends_on definition 13.71 Differentiable curve ¶
      - depends_on definition 13.45 Differentiable map on a topological space ¶
      - depends_on definition 13.48 Differentiable manifold ¶
  - depends_on definition 13.98 $k$-form ¶
    - depends_on definition 13.83 Covector ¶ ↺
    - depends_on definition 13.84 Tensor ¶
      - depends_on definition 13.83 Covector ¶ ↺
      - depends_on definition 13.81 Vector on a manifold ¶ ↺
- 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 ¶

Supports

depends_on definition 25.11 Generators of the Galilei transformations ¶
- depends_on proposition 25.12 The algebra of generators closes ¶

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`	→	Poisson bracket	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:262
`depends_on`	→	Symplectomorphism	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:262
`depends_on`	←	Generators of the Galilei transformations	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:421