λEnter Calculus CompanionRegistered manuscripts, kept distinct

Manuscript V@1 · V.tex · figure · e7ddf37d

Full cubic ordering and joint form limit

Contrast: the Newton–wave cubic form › Fully Wick form and joint cutoff limit · lines 3592–3629

V@1#fig:cubic-form-limit

Back to manuscript
metricscalarrepresented quantumdefect / unresolvedsupport / scope
Stress-only ordering
:AB: C=:ABC:+⟨AC⟩B+⟨BC⟩A:AB:\,C=:ABC:+\langle AC\rangle B+\langle BC\rangle A
Linear contraction remainders. Their unregulated loop restrictions are not covered.
Full cubic ordering
:ABC::ABC: prescribed before cutoff removal
ultraviolet θΛ\theta_\Lambda on all three legs
transfer exclusion cδ(q)c_\delta(\mathbf q)
response-edge profile eϵ(s)e_\epsilon(s)

Metric Cauchy data held fixed.

∣Cf,Λ,δ,ϵ(3)−Cf(3)∣≤Cf(Λ−1+δ+ϵ) p(Ψ)p(X)|\mathcal C^{(3)}_{f,\Lambda,\delta,\epsilon}-\mathcal C_f^{(3)}|\le C_f(\Lambda^{-1}+\delta+\epsilon)\,p(\Psi)p(\Chi)
Joint, profile-independent sesquilinear-form limit on Dϕ\mathscr D_\phi.
self-adjoint unregulated generator
operator on the vacuum

Full cubic ordering and joint form limit. The prescribed cubic Wick ordering subtracts the linear contraction remainders before regulator removal. Ultraviolet, transfer, and response-edge errors converge jointly in the stated Schwartz-domain form bound. This is not an unregulated operator, closability, or spectral-calculus theorem.

Nearby in this section