Proposal for Divergence-Free Quantization of Covariant Scalar Fields

Abstract: Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting models expanded about a suitable pseudofree theory (differing from a free theory by an $\hbar$ term). This procedure not only provides acceptable solutions for models for which no acceptable solution currently exists, e.g., $\phi<sup>4_n$, for spacetime dimension $n\ge4$, but offers a new, divergence-free solution, for less-singular models as well, e.g., $\phi<sup>4_n$, for $n=2,3$.