theorem A.617 Jacobi identity for the Dirac bracket

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 equation 22.46 eq:ham-jacobi ¶
• depends_on lemma A.616 The four identities ¶
  • depends_on equation 26.24 eq:cd-c-matrix ¶
  • depends_on equation 22.46 eq:ham-jacobi ¶ ↺
  • depends_on proposition 25.4 Leibniz rule and derivations ¶
    • depends_on definition 24.14 Hamiltonian vector field ¶
      • depends_on definition 24.8 Symplectic manifold ¶
        • depends_on definition 13.105 Closed form ¶
        • depends_on definition 13.98 $k$-form ¶
        • depends_on definition 24.2 Symplectic vector space ¶
      • depends_on equation 22.4 eq:ham-pdot ¶
      • depends_on equation 22.3 eq:ham-qdot ¶
    • depends_on theorem 25.3 The bracket is a Lie bracket ¶
      • depends_on equation 22.41 eq:ham-poisson-bracket ¶
      • depends_on equation 22.56 eq:ham-symplectic-matrix ¶
      • proves proof ch:08-poisson-quantum-bridge@proof-1 ¶
    • proves proof ch:08-poisson-quantum-bridge@proof-2 ¶
  • proves proof app:A-long-proofs@proof-372 ¶
• proves proof app:A-long-proofs@proof-373 ¶
• proves proof app:A-long-proofs@proof-375 ¶

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