Mixed Models: Combining Incompatible Scalar Models in Any Spacetime Dimension

Abstract

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., $g{\phi }_3^4+g^{\prime }{\phi }_3^6+g^{\prime \prime }{\phi }_3^8$, 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 $g{\phi }_n^4+g^{\prime }{\phi }_n^{138}$, etc., for all $n\ge 3$. Different categories hold for $n=2$ such as, e.g., $gP(\phi {)}_2+g^{\prime }NP(\phi {)}_2$, 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.

14 pages

References in corpus (3)

• Enhanced Quantization: A Primer
• Nontrivial Quantization of ${\varphi }_n^4$, $n\ge 2$
• Matrix Models and Large-N Behavior