remark 26.7 The regularity assumption, stated once
open in the book ·
parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:219
· p. 901
- remark -- no derivation owed by its kind
Rests on
No declared or derived dependency edges point away from this node yet.
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
definition 26.20
Dirac bracket
¶
- depends_on proposition 26.34 Proca constraints are second class ¶ ↺
-
depends_on
proposition 26.13
The first-class functions close
¶
-
depends_on
definition 26.12
First and second class
¶
-
depends_on
lemma A.650
Flattening the constraints
¶
-
depends_on
lemma A.651
Acyclicity of $\delta$
¶
- depends_on proposition A.655 Uniqueness up to a canonical transformation ¶
-
depends_on
theorem A.653
Existence of a nilpotent BRST charge
¶
- depends_on proposition A.655 Uniqueness up to a canonical transformation ¶ ↺
-
depends_on
lemma A.651
Acyclicity of $\delta$
¶
- depends_on proposition 26.13 The first-class functions close ¶ ↺
-
depends_on
proposition 26.10
The four outcomes
¶
- depends_on definition 26.11 The final constraint set ¶ ↺
- 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 theorem 26.51 Existence and uniqueness of the BRST charge ¶
- depends_on proposition 26.48 Consistency of the state conditions ¶
-
depends_on
definition 26.50
The BRST charge
¶
- depends_on theorem 26.17 Counting the physical degrees of freedom ¶ ↺
- depends_on theorem 26.51 Existence and uniqueness of the BRST charge ¶ ↺
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 final constraint set | declared | parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:333 |
depends_on |
← | Flattening the constraints | declared | appendices/A-long-proofs.tex:31651 |
depends_on |
← | The first-class functions close | declared | parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:357 |
depends_on |
← | The four outcomes | declared | parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:276 |
depends_on |
← | Existence and uniqueness of the BRST charge | declared | parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:2074 |