LAUSR

Traditionally, covariant scalar field theory models are either super renormalizable, strictly renormalizable, or nonrenormalizable. The goal of “Mixed Models” is to make sense of sums of these distinct examples, e.g. gφ34 + g′φ 36 + g″φ 38, which includes an example of each kind for space–time dimension n = 3. We show how the several interactions such mixed models have may be turned on and off in any order without any difficulties. Analogous results are shown for gφn4 + g′φ n138, etc. for all n ≥ 3. Different categories hold for n = 2 such as, e.g. gP(φ)2 + g′NP(φ) 2, that involve polynomial (P) and suitable nonpolynomial (NP) interactions, etc. Analogous situations for n = 1 (time alone) offer simple “toy” examples of how such mixed models may be constructed. As a general rule, if the introduction of a specific interaction term reduces the domain of the free classical action, we invariably find that the introduction of the associated quantum interaction leads, effectively, to a “nonrenormalizable” quantu...