  We put forward a finite theory of quantum scattering of fundamental particles
without using auxiliary particles. It suggests that to avoid ultraviolet
divergencies and model faster-than-light effects it suffices to appropriately
change only the free-field Lagrangians while retaining their locality in
space-time and Lorentz invariance. Using functions of two independent
four-vector variables, we base this finite theory on the path-integral
formalism on the four-dimensional space-time and the
Lehmann-Symanzik-Zimmermann reduction formula.
