Manuscript XX-C@1 · XX-C.tex · section · 7a8cab37

Fixed classical clock embeddings

Covariance tails, coordinate pullback, and failure of unconditional infrared control › Fixed classical clock embeddings · lines 1258–1278

Back to manuscript

Let $α$ be a fixed smooth classical inverse coordinate map from the retained perturbation domain. On a compact time interval, assume that outside a ball it has the form

α (τ, x) = (τ, x + β (τ, x)),

with

\partial_{τ}^{m} \partial_{x}^{γ} β = O (∣ x ∣^{- 2 - ∣ γ ∣}),

and that its finite derivative orders needed below are bounded on the remaining region. The original compact classical perturbations and their decaying rods have precisely this asymptotic form for a sufficiently small invertible map.

Displayed formulas in this passage

unlabeled · line 1264
$α (τ, x) = (τ, x + β (τ, x)),$
unlabeled · line 1269
$\partial_{τ}^{m} \partial_{x}^{γ} β = O (∣ x ∣^{- 2 - ∣ γ ∣}),$

Nearby in this section

proposition: Proposition: Classical pullback preserves the proved tail
section: Fixed classical clock embeddings