Destructive interference imposes a cut-off on the ultraviolet Feynman diagram divergence?

In the previous blog post we found a new idea: if we introduce "new" energy to a virtual photon, then there is nothing which would determine the phase of that energy. This implies that destructive interference cancels out any attempt to add such "new energy".

Classical interacting fields: a wave cannot generate waves with a higher frequency

               wave  -->

                   ___             ___

         ____/        \____/        \____   tense string

                        |  |  |  |  |  |       rubber bands

         ________________________    tense string

Above we have two interacting fields: two tense strings. The interaction happens through rubber bands which are tense and attached to both strings.

Intuitively, the interaction cannot produce waves which have a higher frequency than the input wave.

The frequency in quantum mechanics is associated with the particle energy. In a Feynman diagram we have an analogous rule: the energy of the particles coming out of an interaction cannot exceed the input energy.

Can a transient wave in classical interacting fields contain a higher frequency Fourier component? A transient wave is analogous to a virtual, off-shell, particle.

***  WORK IN PROGRESS  ***