definition 26.23 Gauge conditions

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:782 · p. 908

ground object -- no derivation owed

Rests on

depends_on definition 26.20 Dirac bracket ¶
- depends_on definition 22.29 Poisson bracket ¶
  - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.12 Subspace generated by a set of vectors ¶
      - depends_on definition 5.14 Linear independence ¶
  - depends_on definition 22.14 Phase-space coordinate transformation ¶
    - depends_on definition 22.2 Hamiltonian ¶
      - depends_on definition 21.34 Generalized momentum ¶
      - depends_on definition 21.31 Lagrangian ¶
- depends_on proposition 26.19 Second-class constraints come in pairs ¶
  - depends_on definition 26.12 First and second class ¶
    - depends_on definition 26.11 The final constraint set ¶
      - depends_on proposition 26.10 The four outcomes ¶
      - depends_on remark 26.7 The regularity assumption, stated once ¶
    - depends_on definition 22.29 Poisson bracket ¶ ↺
  - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
    - depends_on definition 5.110 Bilinear map ¶
      - depends_on definition 5.37 Linear transformation ¶
    - depends_on definition 5.113 Non-degenerate form ¶
      - depends_on definition 5.110 Bilinear map ¶ ↺
    - depends_on definition 5.111 Symmetric and antisymmetric forms ¶
      - depends_on definition 5.110 Bilinear map ¶ ↺
      - depends_on equation 5.137 eq:lin-bilinear-matrix ¶
    - depends_on equation 5.139 eq:lin-bilinear-congruence ¶
    - proves proof ch:03-linear-algebra-representations@proof-54 ¶
  - proves proof ch:09-constrained-hamiltonian-dynamics@proof-7 ¶
depends_on theorem 26.17 Counting the physical degrees of freedom ¶
- depends_on proposition 26.19 Second-class constraints come in pairs ¶ ↺
- depends_on remark 26.18 The Frobenius theorem is owed by Part II ¶
- depends_on theorem 26.14 First-class constraints generate gauge transformations ¶
  - depends_on definition 26.8 Total Hamiltonian ¶
    - depends_on definition 22.29 Poisson bracket ¶ ↺
    - depends_on proposition 26.6 The canonical Hamiltonian is defined on the constraint surface ¶
      - depends_on equation 26.4 eq:cd-canonical-hamiltonian ¶
      - depends_on proposition 26.5 Primary constraints ¶
      - proves proof ch:09-constrained-hamiltonian-dynamics@proof-2 ¶
  - depends_on proposition 26.10 The four outcomes ¶ ↺
  - proves proof ch:09-constrained-hamiltonian-dynamics@proof-5 ¶
- proves proof ch:09-constrained-hamiltonian-dynamics@proof-6 ¶

Supports

depends_on proposition 26.24 The Faddeev–Popov determinant ¶
- depends_on remark 26.26 What the factor is doing ¶

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`	→	Dirac bracket	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:792
`depends_on`	→	Counting the physical degrees of freedom	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:792
`depends_on`	←	The Faddeev–Popov determinant	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:820