Ervin Goldfain. On Continuous Dimensions and Infrared Mass Generation
Natural Sciences / Physics / Mathematical Physics
Submitted on: Feb 20, 2026, 20:21:35
Description: We show that dimensional regularization of a generic self-interacting field theory with a nearly vanishing mass necessarily induces an infrared mass scale when the running spacetime dimension approaches the critical value D=4. The mechanism is universal and does not rely on spontaneous symmetry breaking alone. Instead, it arises from logarithmic corrections generated by renormalization group (RG) flow near the bifurcation point of beta functions at ϵ≡4-Dâ†'0. We explicitly indicate how dimensional transmutation converts marginal couplings into dynamically generated mass scales. This framework unifies the origin of the Higgs vacuum expectation value and electroweak boson masses with the YangâE"Mills mass gap and the QCD scale I›_QCD. Step-by-step derivations are provided, without appealing to nonperturbative assumptions beyond RG consistency. The paper targets the regime bordering relativistic quantum field theory and complex dynamics.