Scattering in the Absolute Frame Theory: Status and Route

In 1949 Pauli and Villars distinguished a realistic regularization of quantum field theory, whose auxiliary particles belong to the physical theory, from a formalistic one, whose auxiliary masses are mathematical parameters sent to infinity. A framework that claims a physical regulator owes an account of quantum scattering. This note records what the Absolute Frame Theory (AFT) currently establishes about that phenomenon, and what it does not, in four layers. The first is the structural reading of a collision (a reconfiguration of the embedding, with the Born rule derived along the aliasing route under a declared hypothesis). The second is the constructive record (finite-volume reflection positivity, infinite-volume states, clustering below an explicit threshold, and a conditional, Euclidean-restored gauge gap). The third separates the regulator question from the amplitude question. The fourth is five collider-level statements. No new theorem is proved here. The note fixes the route from the Euclidean record to amplitudes (Osterwalder–Schrader reconstruction, Haag–Ruelle asymptotics, and the Lehmann–Symanzik–Zimmermann reduction). It names the three hypotheses on which that route rests, states which parts of each hypothesis companion papers already establish, and separates what is derived from what is conditional and what is open.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-10
DOI
https://doi.org/10.5281/zenodo.24120020
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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preprint

Scattering in the Absolute Frame Theory: Status and Route

Patricio E. Valenzuela
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

Scattering in the Absolute Frame Theory: Status and Route

Patricio E. Valenzuela
preprint en

Abstract

In 1949 Pauli and Villars distinguished a realistic regularization of quantum field theory, whose auxiliary particles belong to the physical theory, from a formalistic one, whose auxiliary masses are mathematical parameters sent to infinity. A framework that claims a physical regulator owes an account of quantum scattering. This note records what the Absolute Frame Theory (AFT) currently establishes about that phenomenon, and what it does not, in four layers. The first is the structural reading of a collision (a reconfiguration of the embedding, with the Born rule derived along the aliasing route under a declared hypothesis). The second is the constructive record (finite-volume reflection positivity, infinite-volume states, clustering below an explicit threshold, and a conditional, Euclidean-restored gauge gap). The third separates the regulator question from the amplitude question. The fourth is five collider-level statements. No new theorem is proved here. The note fixes the route from the Euclidean record to amplitudes (Osterwalder–Schrader reconstruction, Haag–Ruelle asymptotics, and the Lehmann–Symanzik–Zimmermann reduction). It names the three hypotheses on which that route rests, states which parts of each hypothesis companion papers already establish, and separates what is derived from what is conditional and what is open.

Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
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