Top and Higgs Mass from Cancellation Conditions

The success of the electroweak gauge theory [1] has led to a great revival of Quantum Field Theory. By this, however, many theorists do not mean a theory of quantized interacting fields [2]. One rather derives observable results from the "Green's functions" specified by Feynman's integration over classical fields [3], All problems are thus reduced to the choice of the action, which then is evaluated in standard ways (numerically [4] or by perturbation [5])For us who still employ quantized interacting fields, a critical question is how these (and their products) can exist. Is it essential to construct [6] everything with mathematical rigor? Can supergravity remedy the divergencies, or will more recent ideas [7] be needed? Should we admit new physical structures such as a realistic cutoff [8]? Here let us explore the last possibility, since other avenues have been widely discussed. The foundations of fields quantized in our sense shall include: