equation 22.56 eq:ham-symplectic-matrix

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Supports

• depends_on proposition 22.41 Symplectic form of Hamilton's equations ¶
  • depends_on remark 22.42 What the matrix form is for ¶
• depends_on proposition 24.3 Even dimension and the canonical basis ¶
  • depends_on definition 24.4 Symplectic group ¶
    • depends_on proposition 24.5 Properties of the symplectic group ¶
      • depends_on remark 24.6 Connectedness, and what it rests on ¶
      • depends_on remark 24.7 Contrast with the orthogonal group ¶
    • depends_on proposition 24.30 Linear non-squeezing ¶
      • depends_on theorem 24.31 Gromov's non-squeezing theorem ¶
        • depends_on proposition 24.34 Capacities exist if and only if non-squeezing holds ¶
        • depends_on remark 24.35 What non-squeezing does and does not say about nature ¶
  • depends_on proposition 26.25 The Liouville measure of a second-class surface ¶
    • depends_on proposition A.619 The Dirac bracket is a projected Hamiltonian flow ¶
    • depends_on remark 26.26 What the factor is doing ¶
• depends_on remark 24.27 Fixing a scale, so that a ``ball'' means something ¶
  • depends_on definition 24.28 Ball and cylinder ¶
    • depends_on definition 24.33 Symplectic capacity ¶
      • depends_on proposition 24.34 Capacities exist if and only if non-squeezing holds ¶ ↺
    • depends_on example 24.29 A volume-preserving squeeze ¶
    • depends_on proposition 24.30 Linear non-squeezing ¶ ↺
    • depends_on theorem 24.31 Gromov's non-squeezing theorem ¶ ↺
  • depends_on definition 24.33 Symplectic capacity ¶ ↺
• depends_on theorem 25.3 The bracket is a Lie 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 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 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 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 ¶