Ervin Goldfain. Evading Infrared Divergences via Continuous Spacetime Dimensions
Natural Sciences / Physics / Quantum field theory
Submitted on: Mar 13, 2026, 06:55:51
Description: Infrared divergences are a generic feature of gauge theories. In quantum electrodynamics (QED) and quantum chromodynamics (QCD), such divergences are conventionally resolved through cancellation mechanisms associated with BlochâE"Nordsieck (BN) exponentiation and the KinoshitaâE"LeeâE"Nauenberg (KLN) theorem. In this work, we present an alternative resolution of infrared divergences that does not rely on realâE"virtual particle cancellations or summation over degenerate asymptotic states. By formulating field theory in continuous, scale-dependent spatial dimensions, we show that infrared cross sections are no longer singular. We further embed this framework into Fractional Field Theory, pointing out that dimensional flow follows from anomalous transport in momentum space. Finite amplitudes and cross sections are obtained for both Abelian and non-Abelian scattering processes.