On the Convergence of Self-Energy Integrals in a Deformed Local Field Theory

Ultraviolet divergences in perturbative quantum field theory remain a central technical challenge, particularly in self-energy contributions. In this work, we introduce a deformation that is confinedentirely to the interaction sector, while the free theory—including itskinetic term and propagator structure—is left completely unchanged.As a result, the standard notions of causality, unitarity, gauge invariance, and Lorentz invariance are manifestly preserved.Using general power-counting arguments, we demonstrate that themodified interaction structure leads to ultraviolet-finite perturbativeamplitudes to all orders, independently of the detailed functional formof the interaction kernel. In the absence of the interaction scale, thestandard local field theory with pointlike vertices is recovered. Theframework thus provides a conservative and structurally controlledroute to ultraviolet convergence without invoking nonlocal free dynamics or higher-derivative kinetic terms.