Mixed Models: Combining incompatible scalar models in any space time dimension

作者：Klauder John R^*

来源：International Journal of Modern Physics A, 2017, 32(1): 1750001.

DOI：10.1142/S0217751X17500014

• Nonrenormalizable models
• new renormalizable models
• joint renormalizable
• nonrenormalizable models

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(4)(3) + g' phi(6)(3) + g'' phi(8)(3), 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 g phi(4)(n) + g' phi(138)(n), etc. for all n >= 3. Different categories hold for n = 2 such as, e.g. gP(phi)(2) + g' 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. 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" quantum theory. However, in special cases, a classical interaction that does not reduce the domain of the classical free action may generate an "unsatisfactory" quantum theory, which generally involves a model-specific, different approach to become "satisfactory." We will encounter both situations in our analysis.

• 出版日期2017-1-10