λEnter Calculus CompanionRegistered manuscripts, kept distinct

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

Cutoff grammar

Problem, three models, and cutoff grammar › Cutoff grammar · lines 348–396

IV@1#fig:cutoff-grammar

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gravitationalscalaroperator / instrumenterror / restrictionsupport / scope
Model 1
ε\varepsilon
initial-time-edge smoothing
removable
Model 1
fixed TT plane
part of the model
not a regulator
Model 2
R
gravitational IR and UV masks, plus a scalar UV mask
removed at fixed finite M
Model 2
M
total-number compression of the mixed quadratic
retained
Model 2
N
finite-rank gravitational one-particle projection
not particle-number compression
Model 3
Λ\Lambda
retained scalar momentum cutoff
expectation limit only
Model 3
M
retained finite number cutoff
remains in the instrument
R→∞R\to\infty at fixed finite MM, and joint R,NR,N approximation at fixed MM
STOPMeasured M→∞M\to\infty: not asserted.
Λ→∞\Lambda\to\infty selects one finite Λ\Lambda. Expectation only, not an instrument limit.
λ\lambda is numerical interpolation. κ2=0\kappa^2=0 is formal bookkeeping.

Cutoff grammar. The parameters regulate different objects and have different limit statements. Model 1 removes the edge regulator. Model 2 removes spectral masks at fixed number cutoff. Model 3 retains momentum and number cutoffs; its momentum-limit argument concerns coherent expectations only. Finite-rank projection is not particle-number compression.

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