Manuscript IV@1 · IV.tex · section · 351cb2d7

The spectral family

Cutoff ledger: Model 2 › The spectral family · lines 3544–3571

Quantity	Meaning
One-particle measure	$d p$ on TT tensor functions and $d q$ on scalar functions. The mode functions contain the frequency denominators.
$α_{R}$	Gravitational IR and UV mask: one on $R^{- 1} \leq ∣ p ∣ \leq R$ , supported in $(2 R)^{- 1} < ∣ p ∣ < 2 R$ .
$β_{R}$	Scalar UV mask: one on $∣ q ∣ \leq R$ , supported in $∣ q ∣ < 2 R$ .
$M$	Total particle-number cutoff on the mixed quadratic.
Free-term cutoff	Scalar number cutoff only; it must not depend on gravitational particle number.
$N$	Finite-rank projection of gravitational kernel legs.