proposition A.619 The Dirac bracket is a projected Hamiltonian flow

Rests on

• depends_on equation 26.42 eq:cd-reduced-projector ¶
• depends_on equation 24.7 eq:sym-bracket ¶
• 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 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 definition 7.97 Partial derivative; gradient ¶
        • depends_on definition 22.14 Phase-space coordinate transformation ¶
    • depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶ ↺
    • proves proof ch:09-constrained-hamiltonian-dynamics@proof-7 ¶
  • 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 ¶
• proves proof app:A-long-proofs@proof-374 ¶

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