notation 26.1 Weak and strong equality

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:73 · p. 899

notation -- no derivation owed by its kind

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 notation 22.1 not:ham-indices ¶

Supports

depends_on notation 26.28 Field systems ¶
- depends_on definition 26.40 The $3+1$ decomposition ¶
  - depends_on lemma A.623 The adapted frame of the $3+1$ split ¶
    - depends_on lemma A.626 Decomposition of $\nabla n$, and the acceleration ¶
      - depends_on lemma A.630 Codazzi equation ¶
      - depends_on lemma A.631 The normal–normal Ricci contraction ¶
  - depends_on proposition 26.41 The ADM form of the Einstein–Hilbert Lagrangian ¶
    - depends_on theorem 26.42 The Hamiltonian structure of general relativity ¶
      - depends_on notation A.636 Densities and smearing ¶
      - depends_on proposition 26.43 The hypersurface-deformation algebra ¶
- depends_on notation A.636 Densities and smearing ¶ ↺
- depends_on notation 26.36 Gauge fields and their SI dimensions ¶
  - depends_on proposition 26.37 Constraint structure of Yang–Mills theory ¶

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/09-constrained-hamiltonian-dynamics.tex:85
`depends_on`	→	not:ham-indices	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:85
`depends_on`	←	Field systems	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1049