remark 26.4 The constant-rank theorem is owed by Part II
open in the book ·
parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:123
· p. 900
- remark -- no derivation owed by its kind
Rests on
No declared or derived dependency edges point away from this node yet.
Supports
-
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 26.5
Primary constraints
¶
-
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
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
definition 26.8
Total Hamiltonian
¶
-
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 113.3 Degrees of freedom before and after ¶
- 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
proposition 26.6
The canonical Hamiltonian is defined on the constraint
surface
¶
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 |
← | Flattening the constraints | declared | appendices/A-long-proofs.tex:31651 |
depends_on |
← | Primary constraints | declared | parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:152 |