Regularization by asymptotic subtraction: a constructive approach

We propose a scheme to regularize divergent integrals in quantum field theory based on a new asymptotic subtraction method. The framework builds on the structural decomposition of the integrand asymptotic expansion, which distinguishes between contributions that drive ultraviolet singularities and those that remain finite. This asymptotic subtraction method isolates the genuinely singular sector and enables a consistent subtraction of divergences while maintaining covariance and gauge symmetry. In single-scale theories, we show that the renormalized quantities exhibit a logarithmic dependence on the physical scale uniquely determined by the ultraviolet asymptotics, offering a derivation of logarithmic terms that is independent of standard renormalization-group flows. Because it relies only on the asymptotic structure rather than on a standard relativistic power counting, the method is naturally applicable to theories with modified dispersion relations and nonstandard ultraviolet scaling. Although formulated here for ultraviolet divergences, the underlying strategy extends straightforwardly to infrared singularities.