Finiteness of Closed-Loop Integrals in Other Interaction Models of Algebraic QFT

Determine whether closed-loop integrals in Feynman diagrams remain finite for other physically relevant interaction models formulated within the algebraic quantum field theory for structureless elementary particles (the structureless sector of Structural Algebraic Quantum Field Theory), thereby establishing whether renormalization-free behavior persists beyond the specific model instances analyzed.

Background

The paper proposes an algebraic quantum field theory for structureless elementary particles in which fields are represented in energy space via orthogonal spectral polynomials satisfying a three-term recursion relation. In this framework, orthogonality and completeness properties replace differential equations and yield canonical commutation relations and simple constructions of propagators.

A central claim is that, in the interacting theory, closed-loop integrals appearing in Feynman diagrams are finite, eliminating the need for renormalization. This is illustrated through sample diagrams and numerical evaluations in a specific scalar–spinor interaction model, with evidence that finiteness continues to higher-order loops. The authors explicitly note uncertainty about whether this finiteness extends to other physically relevant interaction models within the same algebraic QFT framework.