High-gradient theories as new essential ingredient for the beyond-Standard-Model Des(s)ert cuisine: Getting rid of divergences in Feynman graphs, unified ``all-in-one'' states and origin of generations

Inspiring ourselves by the assumption that the notion of symmetry itself is insufficient to construct the consistent physics of the Desert (the so-called region of energies beyond the Standard Model) and some additional insights are needed, we suggests that high-energy theories must take into account the higher-order variations of fields. With this in mind we propose the generalization of the concepts of kinetic energy and free particle. It is shown that the theory founded on such principles reveals major features of the genuinely high-energy one, first of all, it appears to be free from ultra-violet divergences, even the self-energy loop terms become finite. Also we discuss other arising interesting phenomena such as the high-gradient currents and charges, unified ``all-in-one’’ multi-mass states, VR symmetry, regularization-without-renormalization of SM, etc.