definition 26.9 Consistency conditions

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:254 · p. 901

ground object -- no derivation owed

Rests on

depends_on equation 26.7 eq:cd-evolution ¶
depends_on equation 26.2 eq:cd-primary ¶

Supports

depends_on proposition 26.10 The four outcomes ¶
- depends_on definition 26.11 The final constraint set ¶
  - 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 proposition 26.24 The Faddeev–Popov determinant ¶
      - depends_on proposition 26.25 The Liouville measure of a second-class surface ¶
      - depends_on theorem 26.17 Counting the physical degrees of freedom ¶
      - depends_on theorem 26.21 Properties of the Dirac bracket ¶
    - depends_on proposition 26.34 Proca constraints are second class ¶
      - depends_on proposition 113.3 Degrees of freedom before and after ¶
- 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 theorem 26.42 The Hamiltonian structure of general relativity ¶
  - depends_on notation A.636 Densities and smearing ¶
    - depends_on lemma A.637 Closed form of $H_{\parallel}$, and what it generates ¶
      - depends_on lemma A.638 Naturality ¶
  - depends_on proposition 26.43 The hypersurface-deformation algebra ¶ ↺
- 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 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 26.17 Counting the physical degrees of freedom ¶ ↺

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-evolution	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:260
`depends_on`	→	eq:cd-primary	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:260
`depends_on`	←	The four outcomes	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:276