remark 26.26 What the factor is doing

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:988 · p. 910

remark -- no derivation owed by its kind

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depends_on proposition 26.24 The Faddeev–Popov determinant ¶
- depends_on definition 26.23 Gauge conditions ¶
  - 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 22.14 Phase-space coordinate transformation ¶
    - depends_on proposition 26.19 Second-class constraints come in pairs ¶
      - depends_on definition 26.12 First and second class ¶
      - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
      - 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 proposition 26.10 The four outcomes ¶
      - proves proof ch:09-constrained-hamiltonian-dynamics@proof-5 ¶
    - proves proof ch:09-constrained-hamiltonian-dynamics@proof-6 ¶
- depends_on proposition 26.19 Second-class constraints come in pairs ¶ ↺
- proves proof ch:09-constrained-hamiltonian-dynamics@proof-10 ¶
depends_on proposition 26.25 The Liouville measure of a second-class surface ¶
- depends_on definition 24.20 Liouville volume ¶
  - depends_on definition 13.102 Wedge product ¶
    - depends_on definition 13.98 $k$-form ¶
      - depends_on definition 13.83 Covector ¶
      - depends_on definition 13.84 Tensor ¶
    - depends_on equation 13.239 eq:mfd-dual-basis ¶
  - depends_on definition 24.8 Symplectic manifold ¶
    - depends_on definition 13.105 Closed form ¶
      - depends_on definition 13.103 Exterior derivative ¶
      - depends_on definition 13.98 $k$-form ¶ ↺
    - depends_on definition 13.98 $k$-form ¶ ↺
    - depends_on definition 24.2 Symplectic vector space ¶
      - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶ ↺
  - depends_on theorem 24.12 Darboux ¶
    - depends_on definition 24.8 Symplectic manifold ¶ ↺
    - depends_on theorem A.68 Darboux ¶
      - depends_on definition A.67 Symplectic manifold ¶
      - depends_on equation 5.144 eq:lin-symplectic-normal-form ¶
      - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶ ↺
      - proves proof app:A-long-proofs@proof-57 ¶
    - proves proof ch:07-symplectic-geometry@prooflink-1 ¶
- depends_on proposition 26.19 Second-class constraints come in pairs ¶ ↺
- depends_on proposition 24.3 Even dimension and the canonical basis ¶
  - depends_on definition 24.2 Symplectic vector space ¶ ↺
  - depends_on equation 22.56 eq:ham-symplectic-matrix ¶
  - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶ ↺
  - proves proof ch:07-symplectic-geometry@proof-1 ¶
- proves proof ch:09-constrained-hamiltonian-dynamics@proof-11 ¶

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type	direction	node	provenance	where
`depends_on`	→	The Faddeev–Popov determinant	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1004
`depends_on`	→	The Liouville measure of a second-class surface	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1004