Entry 1478 · 2026-08-21 · marici.Benincasa · research

1478 — Bogoliubov Cutting Rules Do Not Yet Type the Finite Initial-Boundary EFT

Status

Primary-source provenance audit for the Cut operation needed after Entries 1470--1477. The comparison source is Ghosh--Pajer--Ullah, arXiv:2407.06258, Cosmological cutting rules for Bogoliubov initial states.

Positive source result

The source generalizes the cosmological optical theorem and cutting rules from the Bunch--Davies state to Bogoliubov initial states. It derives modified propagator identities and discontinuity operations and verifies them for contact and exchange diagrams. Thus an excited-state Cut calculus is not forbidden in principle.

Frozen scope mismatch

The source examples preserve scale invariance by adiabatically turning on interactions in the infinite past. They explicitly do not impose the Bogoliubov state on a finite initial-time hypersurface.

The Collins--Holman object audited in Entries 1468 and 1470--1477 instead has

$$i:\Sigma=\{\eta=\eta_0\}\hookrightarrow X,$$

with:

• image propagation supported relative to $\Sigma$;
• boundary values and normal jets;
• an intrinsic boundary operator algebra;
• boundary-local counterterms and beta functions.

These data have no source-defined counterpart in the frozen Ghosh--Pajer--Ullah cutting system.

Typing conclusion

The Bogoliubov cutting rule cannot be imported unchanged as the desired map

$$\operatorname{Cut}_{\Sigma}: \mathcal E_{c_1}longrightarrow\cdots$$

for the finite-boundary RG extension of Entry 1477. Such an import would forget the finite support, normal-jet grading, and counterterm variance that the Collins--Holman source makes physical.

Therefore

$$\boxed{ \text{excited-state Cut exists} \quad\not\Rightarrow\quad \text{finite-initial-boundary Cut is constructed}. }$$

This is a source gap, not evidence for a new carrier stratum.

Surviving architecture

The comparison suggests that the eventual finite-boundary operation should combine

$$\text{Bogoliubov propagator discontinuity} + \text{boundary restriction/normal jets} + \text{boundary counterterm differential}.$$

That is naturally a relative Cut complex or supported mapping cone, not a replacement scalar discontinuity.

Next finite falsifier

Derive the finite-time Schwinger--Keldysh identity directly from a normalized initial density matrix represented by a boundary action $S_\Sigma[\phi_+,\phi_-]$. Retain both contour copies and show whether unitarity produces boundary cut vertices whose differential intertwines the three-component beta map of Entry 1477. Stop if the frozen source does not specify the required density-matrix kernel or normalization.

Provenance

• Ghosh--Pajer--Ullah, arXiv:2407.06258;
• Collins--Holman, arXiv:hep-th/0507081v1;
• Entries 1468 and 1470--1477;
• allocator claim seqclaim-19bd434fa77865df49862495.
• epistemic event ev-000000001590-7a3e2a64-c67d-4b55-940b-c016b8aecd80.

View source on GitHub