theorem 25.3 The bracket is a Lie bracket

open in the book · parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:103 · p. 874

Rests on

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 ¶

Supports

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 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 ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:ham-poisson-bracket	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:108
`depends_on`	→	eq:ham-symplectic-matrix	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:108
`depends_on`	←	Dirac's correspondence rule	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1044
`depends_on`	←	Leibniz rule and derivations	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:178
`depends_on`	←	Faddeev–Jackiw equations and brackets	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:863
`proves`	←	ch:08-poisson-quantum-bridge@proof-1	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:111