proposition 26.6 The canonical Hamiltonian is defined on the constraint surface

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:183 · p. 901

Rests on

depends_on equation 26.4 eq:cd-canonical-hamiltonian ¶
depends_on proposition 26.5 Primary constraints ¶
- depends_on definition 26.3 Singular Lagrangian ¶
  - depends_on equation 22.2 eq:ham-hessian ¶
  - depends_on proposition 22.3 Invertibility of the Legendre map ¶
    - depends_on corollary A.292 Inverse function theorem ¶
      - depends_on proposition 7.104 Chain rule in several variables ¶
      - depends_on theorem A.286 Implicit function theorem ¶
      - proves proof app:A-long-proofs@proof-186 ¶
    - depends_on equation 21.43 eq:lag-generalized-momentum ¶
    - proves proof ch:05-hamiltonian-mechanics@proof-1 ¶
- depends_on remark 26.4 The constant-rank theorem is owed by Part II ¶
- proves proof ch:09-constrained-hamiltonian-dynamics@proof-1 ¶
proves proof ch:09-constrained-hamiltonian-dynamics@proof-2 ¶

Supports

depends_on definition 26.8 Total Hamiltonian ¶
- depends_on definition 26.16 Extended Hamiltonian ¶
- depends_on theorem 26.21 Properties of the Dirac bracket ¶
  - depends_on postulate 26.47 Dirac quantization ¶
    - depends_on definition 26.50 The BRST charge ¶
      - depends_on notation A.646 Gradings and brackets ¶
      - depends_on theorem 26.51 Existence and uniqueness of the BRST charge ¶
    - depends_on proposition 26.48 Consistency of the state conditions ¶
- depends_on theorem 26.14 First-class constraints generate gauge transformations ¶
  - depends_on definition 26.16 Extended Hamiltonian ¶ ↺
  - depends_on postulate 26.47 Dirac quantization ¶ ↺
  - depends_on theorem 26.17 Counting the physical degrees of freedom ¶
    - depends_on corollary A.642 The constraints are first class ¶
    - depends_on definition 26.23 Gauge conditions ¶
      - depends_on proposition 26.24 The Faddeev–Popov determinant ¶
    - depends_on proposition 26.32 Constraint structure of the free Maxwell field ¶
      - depends_on proposition 26.34 Proca constraints are second class ¶
      - depends_on proposition 26.37 Constraint structure of Yang–Mills theory ¶
    - depends_on proposition 26.34 Proca constraints are second class ¶ ↺
    - depends_on proposition 26.29 Reparametrization invariance and the mass-shell constraint ¶
    - 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 ¶

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:cd-canonical-hamiltonian	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:193
`depends_on`	→	Primary constraints	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:193
`depends_on`	←	Total Hamiltonian	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:246
`proves`	←	ch:09-constrained-hamiltonian-dynamics@proof-2	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:196