definition 25.42 Ordering rule

open in the book · parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1566 · p. 890

ground object -- no derivation owed

Rests on

depends_on corollary 25.41 Quantization is not a functor ¶
- depends_on theorem 25.38 Groenewold–van Hove ¶
  - depends_on equation 25.31 eq:pq-dirac-rule ¶
  - depends_on theorem 25.34 Stone–von Neumann ¶
    - depends_on definition 12.64 Strongly continuous one-parameter unitary group ¶
      - depends_on definition 12.41 The operator classes ¶
      - depends_on definition 6.6 Continuous map ¶
    - depends_on equation 25.33 eq:pq-ccr ¶
    - depends_on theorem 12.66 Stone ¶
      - depends_on definition 12.64 Strongly continuous one-parameter unitary group ¶ ↺
      - depends_on proposition 12.65 Exponential of a bounded self-adjoint operator ¶
      - depends_on theorem 12.59 Spectral theorem for a bounded self-adjoint operator ¶
      - proves proof ch:10-hilbert-spaces@prooflink-3 ¶
    - proves proof ch:08-poisson-quantum-bridge@prooflink-1 ¶
  - depends_on theorem 5.160 Schur's second lemma ¶
    - depends_on definition 5.53 Isomorphism ¶
      - depends_on definition 5.37 Linear transformation ¶
    - depends_on definition 5.145 Equivalent representations ¶
      - depends_on definition 5.141 Representation of a group ¶
    - depends_on definition 5.147 Invariant subspace ¶
      - depends_on definition 5.7 Vector subspace ¶
      - depends_on definition 5.141 Representation of a group ¶ ↺
    - depends_on definition 5.148 Irreducible representation ¶
      - depends_on definition 5.147 Invariant subspace ¶ ↺
    - proves proof ch:03-linear-algebra-representations@proof-68 ¶
  - proves proof ch:08-poisson-quantum-bridge@proof-16 ¶
depends_on postulate 25.27 Dirac's correspondence rule ¶
- 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 25.44 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 lemma A.607 A zero-free entire function is an exponential ¶
- 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 ¶

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`	→	Quantization is not a functor	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1575
`depends_on`	→	Dirac's correspondence rule	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1575
`depends_on`	←	Weyl and normal ordering	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1629
`depends_on`	←	The size of the ambiguity	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1593