Manuscript IX-E@1 · IX-E.tex · section · 8f8d5e7f

The complete first-stage commutator calculation

E1: ordered-data consistency › The complete first-stage commutator calculation · lines 581–600

IX-E@1#eq:locked-q

The locked first-stage coefficients are

Q_{f, g} Q^{R}_{g, f} = - 2 ⟨ f (x) g (y) K (x, y), \partial_{t} ϕ (x) h_{00} (y) ⟩, = - 2 ⟨ g (y) f (x) K (x, y), h_{00} (y) \partial_{t} ϕ (x) ⟩ .

The brackets denote the supplied distributional pairing, including its configuration arguments. Classical configuration factors commute; no interchange of singular distributions is being made.

Displayed formulas in this passage

IX-E@1#eq:locked-q · line 584
$Q_{f, g} Q^{R}_{g, f} = - 2 ⟨ f (x) g (y) K (x, y), \partial_{t} ϕ (x) h_{00} (y) ⟩, = - 2 ⟨ g (y) f (x) K (x, y), h_{00} (y) \partial_{t} ϕ (x) ⟩ .$

Nearby in this section

proposition: Proposition: First-stage commutator
section: The complete first-stage commutator calculation
lemma: Lemma: Compact detection
section: The complete first-stage commutator calculation
theorem: Theorem: Fixed-domain obstruction
section: The complete first-stage commutator calculation
proposition: Proposition: Classical multiplication is not a solution
section: The complete first-stage commutator calculation