equation 22.41 eq:ham-poisson-bracket

Rests on

No declared or derived dependency edges point away from this node yet.

Supports

• depends_on definition 25.50 Star product and Moyal bracket ¶
• depends_on postulate 25.27 Dirac's correspondence rule ¶
  • depends_on definition 25.42 Ordering rule ¶
    • depends_on definition 25.44 Weyl and normal ordering ¶
      • depends_on definition 25.50 Star product and Moyal bracket ¶ ↺
      • depends_on definition 25.52 Wigner function ¶
        • depends_on definition A.605 The analytic continuation of the overlaps ¶
      • depends_on example 25.45 Weyl ordering collapses ¶
      • depends_on proposition 25.46 Normal ordering disagrees already at degree two ¶
    • depends_on proposition 25.43 The size of the ambiguity ¶
      • depends_on proposition 25.48 Where the ambiguity does and does not bite ¶
  • depends_on postulate 26.47 Dirac quantization ¶
    • depends_on definition 26.50 The BRST charge ¶
      • depends_on notation A.646 Gradings and brackets ¶
        • depends_on definition A.647 Koszul–Tate differential ¶
        • depends_on lemma A.652 Nilpotency, order by order ¶
      • depends_on theorem 26.51 Existence and uniqueness of the BRST charge ¶
    • depends_on proposition 26.48 Consistency of the state conditions ¶
  • depends_on proposition 25.29 Canonical commutation relations ¶
  • depends_on proposition 25.31 The Heisenberg equation is the evolution equation ¶
  • depends_on proposition 25.25 Noncommuting coordinates and the Landau degeneracy ¶
• depends_on theorem 22.34 Evolution of a phase-space function ¶
  • depends_on corollary 22.35 cor:ham-evolution-static ¶
    • depends_on proposition 22.37 Constants of motion ¶
  • depends_on remark 22.36 The whole dynamics in one operation ¶
  • depends_on theorem 22.38 Poisson's theorem ¶
    • depends_on proposition 25.12 The algebra of generators closes ¶
    • depends_on remark 22.39 Poisson's theorem does not manufacture new constants ¶
• depends_on theorem 23.31 Liouville–Arnold ¶
  • depends_on proposition 24.56 The Bohr–Sommerfeld condition is a triviality condition on the prequantum holonomy ¶
    • depends_on remark 24.57 The half-integer, and the honest status of the construction ¶
  • depends_on remark 23.33 Integrability is exceptional ¶
  • depends_on remark 23.32 What that proof imports ¶
  • depends_on theorem 32.51 Kolmogorov–Arnold–Moser, quoted ¶
    • depends_on phenomenon 32.58 Regular and chaotic motion coexist ¶
    • depends_on phenomenon 32.59 The solar system is chaotic ¶
    • depends_on remark 23.33 Integrability is exceptional ¶ ↺
  • depends_on theorem 32.47 Poincaré's non-integrability, quoted ¶
• depends_on theorem 25.3 The bracket is a Lie bracket ¶
  • depends_on postulate 25.27 Dirac's correspondence rule ¶ ↺
  • depends_on proposition 25.4 Leibniz rule and derivations ¶
    • depends_on lemma A.616 The four identities ¶
      • depends_on theorem A.617 Jacobi identity for the Dirac bracket ¶
  • depends_on theorem 25.22 Faddeev–Jackiw equations and brackets ¶
    • depends_on example 25.24 A charged particle in a strong magnetic field ¶