Manuscript Psy02-A@1 · Psy02-A.tex · section · d92ce402

An explicit extension and complete ambiguity in its class

A separate normalization-independent response benchmark › An explicit extension and complete ambiguity in its class · lines 1636–1655

Psy02-A@1#eq:finite-part

Choose a smooth compactly supported function $χ : [0, \infty) \to R$ , equal to one near zero. For real $F \in C_{c}^{\infty} (R^{4})$ , define

⟨ R_{χ}, F ⟩ = \frac{γ}{4} \int_{0}^{\infty} \int_{S^{2}} [\frac{F ( t , t ω ) - χ ( t ) F ( 0 )}{t} + \partial_{r} F (t, r ω)_{r = t}] d ω d t .

The cutoff includes its chosen reference time unit.

Displayed formulas in this passage

Psy02-A@1#eq:finite-part · line 1641
$⟨ R_{χ}, F ⟩ = \frac{γ}{4} \int_{0}^{\infty} \int_{S^{2}} [\frac{F ( t , t ω ) - χ ( t ) F ( 0 )}{t} + \partial_{r} F (t, r ω)_{r = t}] d ω d t .$