definition 26.11 The final constraint set

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:321 · p. 902

ground object -- no derivation owed

Rests on

depends_on proposition 26.10 The four outcomes ¶
- depends_on definition 26.9 Consistency conditions ¶
  - depends_on equation 26.7 eq:cd-evolution ¶
  - depends_on equation 26.2 eq:cd-primary ¶
- depends_on remark 26.7 The regularity assumption, stated once ¶
- proves proof ch:09-constrained-hamiltonian-dynamics@proof-3 ¶
depends_on remark 26.7 The regularity assumption, stated once ¶ ↺

Supports

depends_on definition 26.12 First and second class ¶
- depends_on proposition 26.13 The first-class functions close ¶
  - depends_on proposition 26.43 The hypersurface-deformation algebra ¶
  - depends_on proposition 26.37 Constraint structure of Yang–Mills theory ¶
- depends_on proposition 26.19 Second-class constraints come in pairs ¶
  - depends_on definition 26.20 Dirac bracket ¶
    - depends_on definition 26.23 Gauge conditions ¶
      - depends_on proposition 26.24 The Faddeev–Popov determinant ¶
    - depends_on example 26.22 Holonomic constraints ¶
    - depends_on theorem A.617 Jacobi identity for the Dirac bracket ¶
    - depends_on theorem 26.21 Properties of the Dirac bracket ¶
      - depends_on postulate 26.47 Dirac quantization ¶
  - depends_on proposition 26.24 The Faddeev–Popov determinant ¶ ↺
  - depends_on proposition 26.25 The Liouville measure of a second-class surface ¶
    - depends_on proposition A.619 The Dirac bracket is a projected Hamiltonian flow ¶
    - depends_on remark 26.26 What the factor is doing ¶
  - 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 26.37 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 ¶ ↺
  - depends_on theorem 26.21 Properties of the Dirac bracket ¶ ↺
- depends_on proposition 26.34 Proca constraints are second class ¶ ↺

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`	→	The four outcomes	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:333
`depends_on`	→	The regularity assumption, stated once	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:333
`depends_on`	←	First and second class	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:350