notation 26.28 Field systems

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1026 · p. 910

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 26.1 Weak and strong equality ¶
- depends_on definition 22.29 Poisson bracket ¶ ↺
- depends_on notation 22.1 not:ham-indices ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Poisson bracket	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1049
`depends_on`	→	Weak and strong equality	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1049
`depends_on`	←	The $3+1$ decomposition	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1582
`depends_on`	←	Densities and smearing	declared	appendices/A-long-proofs.tex:30969
`depends_on`	←	Gauge fields and their SI dimensions	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1409