proposition 26.10 The four outcomes

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:263 · p. 901

Rests on

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 ¶

Supports

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 definition 26.23 Gauge conditions ¶
      - 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 proposition 26.24 The Faddeev–Popov determinant ¶
      - depends_on remark 26.26 What the factor is doing ¶
    - 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 26.29 Reparametrization invariance and the mass-shell constraint ¶
      - depends_on theorem 26.42 The Hamiltonian structure of general relativity ¶
    - depends_on theorem 26.21 Properties of the Dirac bracket ¶ ↺
  - depends_on proposition 26.34 Proca constraints are second class ¶ ↺
depends_on proposition 26.32 Constraint structure of the free Maxwell field ¶ ↺
depends_on theorem 26.42 The Hamiltonian structure of general relativity ¶ ↺
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 definition A.647 Koszul–Tate differential ¶
      - depends_on lemma A.652 Nilpotency, order by order ¶
    - 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`	→	Consistency conditions	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:276
`depends_on`	→	The regularity assumption, stated once	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:276
`depends_on`	←	The final constraint set	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:333
`depends_on`	←	Constraint structure of the free Maxwell field	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1174
`depends_on`	←	The Hamiltonian structure of general relativity	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1649
`depends_on`	←	First-class constraints generate gauge transformations	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:411
`proves`	←	ch:09-constrained-hamiltonian-dynamics@proof-3	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:279