A registered result in its source context
Original ledger classification: Bridge [E] (LSZ structure + one-loop optical theorem) + [C] (gap/Z) + [O] (gravity ghost)
Recorded statement: S_pert -> S_phys LSZ BRIDGE + ONE-LOOP UNITARITY (2026-06-18): connects the EG perturbative S-matrix (v269/v271/v273) to the physical asymptotic S-matrix (S_phys = LSZ on the OS-reconstructed Wightman functions, v240); the three-layer…
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Paper context: tfpt research contracts
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QFT4D.SPERT.04
Original ledger classification: Bridge [E] (LSZ structure + one-loop optical theorem) + [C] (gap/Z) + [O] (gravity ghost)
Original claim text
S_pert -> S_phys LSZ BRIDGE + ONE-LOOP UNITARITY (2026-06-18): connects the EG perturbative S-matrix (v269/v271/v273) to the physical asymptotic S-matrix (S_phys = LSZ on the OS-reconstructed Wightman functions, v240); the three-layer S-matrix is now S_top (v243) | S_pert (v269) --LSZ--> S_phys (v240). [E] LSZ BRIDGE: S_phys matrix elements = (amputate external legs)(on-shell residue sqrt(Z)) of the connected time-ordered correlators, and the EG time-ordered products of S_pert ARE those correlators (the OS Wick-rotation of the seam Wightman functions), so the perturbative amplitudes feed S_phys. [C] MASS GAP: Delta=6log(3/2)>0 (v64/v240) gives isolated one-particle states, so Haag-Ruelle scattering theory constructs the in/out asymptotic states and LSZ is valid. [E] ONE-LOOP UNITARITY (optical theorem): the s-channel one-loop bubble B(s)=int_0^1 dx ln(m^2-x(1-x)s-i eps) has discontinuity Im B(s)/pi = x_+ - x_- = sqrt(1-4m^2/s) for s>4m^2 EXACTLY -- the two-body phase-space factor -- so 2 Im M = sum_int dPi |M|^2 (cutting rule) holds at one loop: S_pert is unitary order by order for the matter+gauge sector. [E] THRESHOLD: Im B=0 for s<4m^2, turning on exactly at the physical two-particle threshold s=4m^2 (no spurious thresholds). [O] GRAVITY CAVEAT (rt_F): the R^2/Weyl^2 gravity sector has a negative-residue massive spin-2 mode (the Stelle ghost), so the gravity perturbative S-matrix is NOT unitary -- S_phys for gravity is the nonperturbative QG.AMB.01 frontier. [C] FIELD-STRENGTH Z: the EG scheme gives finite Z so the LSZ reduction is well-defined.
Original classification detail
[E] the LSZ bridge structure + the one-loop optical theorem (exact: cut = two-body phase space) + the threshold analyticity; [C] the gap->asymptotic-states link + finite Z; [O] the gravity ghost (-> QG.AMB.01). Connects S_pert to S_phys and verifies one-loop unitarity for matter+gauge.
Dependencies as recorded
QFT4D.SPERT.01; QFT4D.SPERT.02; DYN.GNS.01; DHR.SMATRIX.01; REDTEAM.F.01
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- Research contracts
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- 2026-06-18 (4D QFT: the [formula in source] LSZ bridge [formula in source] one-loop unitarity, v278)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
Navigation through a shared verification script
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- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- 2026-06-23 (External-review closure: the two genuine residual targets named — v381 the all-order Epstein–Glaser/BRST contract for [formula in source] , and v382 the Quillen determinant-line variation as a tracked target)Research changelog; TFPT — Introduction and reading guide
- 2026-06-19 (an infinite-derivative narrowing of the Stelle-ghost attack, the double-pushout figure, and the ``constancy of [formula in source] '' framing of SEAM.EQUIV.01: v304)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v278_lsz_bridge_unitarity.pyRegistered verification module · registry
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QFT4D.SPERT.04 — the S_pert → S_phys LSZ bridge + one-loop unitarity: connects the EG perturbative S-matrix (v269/v271/v273) to the physical asymptotic S-matrix (S_phys = LSZ on the OS Wightman functions, v240). [E] LSZ bridge: S_phys = amputate+on-shell-residue of the connected time-ordered products, and the EG T-products of S_pert ARE those correlators (OS Wick-rotation, v240) → S_pert --LSZ--> S_phys; [C] the gap Δ=6log(3/2)>0 gives Haag-Ruelle asymptotic states so LSZ is valid; [E] ONE-LOOP UNITARITY (optical theorem): the bubble discontinuity Im B(s)/π = x₊−x₋ = √(1−4m²/s) EXACTLY = the two-body phase space, so 2 Im M = ∑∫dΠ|M|² (cutting rule) holds → matter+gauge unitary; [E] threshold: Im B=0 below s=4m², turns on at the physical 2-particle threshold; [O] gravity caveat — the Stelle ghost makes the gravity perturbative S-matrix non-unitary → QG.AMB.01; [C] finite field-strength Z from the EG scheme. Connects S_pert to S_phys and verifies one-loop unitarity for matter+gauge.
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