Mixed Models: Combining Incompatible Scalar Models in Any Spacetime Dimension

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., $g\varphi^4_3+g'\varphi^6_3+g''\varphi^8_3$, which includes an example of each kind for spacetime 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 $g\varphi^4_n+g'\varphi^{138}_n$, etc., for all $n\ge3$. Different categories hold for $n=2$ such as, e.g., ${g P(\varphi)_2+g' N\!P}(\varphi)_2$, that involve polynomial ($P$) and suitable nonpolynomial ($N\!P$) interactions, etc. Analogous situations for $n=1$ (time alone) offer simple toy’ examples of how such mixed models may be constructed.