proposition 26.5 Primary constraints

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:142 · p. 900

Rests on

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 definition 7.13 Composite function ¶
      - depends_on definition 7.99 Differentiability at a point ¶
      - depends_on definition 7.102 Differential of a function ¶
      - proves proof ch:05-real-analysis@proof-63 ¶
    - depends_on theorem A.286 Implicit function theorem ¶
      - depends_on definition 7.99 Differentiability at a point ¶ ↺
      - depends_on proposition 7.104 Chain rule in several variables ¶ ↺
      - depends_on theorem 7.100 $C^{1}$ implies differentiable ¶
      - proves proof app:A-long-proofs@proof-185 ¶
    - 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 ¶

Supports

depends_on proposition 26.6 The canonical Hamiltonian is defined on the constraint surface ¶
- 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 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 26.32 Constraint structure of the free Maxwell field ¶
      - 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 proposition 26.32 Constraint structure of the free Maxwell field ¶ ↺
depends_on proposition 26.29 Reparametrization invariance and the mass-shell constraint ¶ ↺

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`	→	Singular Lagrangian	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:152
`depends_on`	→	The constant-rank theorem is owed by Part II	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:152
`depends_on`	←	The canonical Hamiltonian is defined on the constraint surface	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:193
`depends_on`	←	Constraint structure of the free Maxwell field	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1174
`depends_on`	←	Reparametrization invariance and the mass-shell constraint	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1071
`proves`	←	ch:09-constrained-hamiltonian-dynamics@proof-1	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:155