postulate 25.27 Dirac's correspondence rule

open in the book · parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1036 · p. 884

ground object -- no derivation owed

Rests on

depends_on equation 22.41 eq:ham-poisson-bracket ¶
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 ¶

Supports

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 lemma A.606 $F$ is entire, and is the overlap in disguise ¶
  - 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.651 Acyclicity of $\delta$ ¶
      - depends_on lemma A.648 $\delta$ is the ghost bracket with $\Omega_{(0)}$, and $\delta^{2}=0$ ¶
    - depends_on lemma A.652 Nilpotency, order by order ¶
      - depends_on proposition A.654 The Yang–Mills case ¶
      - depends_on proposition A.655 Uniqueness up to a canonical transformation ¶
      - depends_on theorem A.653 Existence of a nilpotent BRST charge ¶
  - 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 ¶

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:1044
`depends_on`	→	The bracket is a Lie bracket	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1044
`depends_on`	←	Ordering rule	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1575
`depends_on`	←	Dirac quantization	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1834
`depends_on`	←	Canonical commutation relations	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1094
`depends_on`	←	The Heisenberg equation is the evolution equation	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1143
`depends_on`	←	Noncommuting coordinates and the Landau degeneracy	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:983