Proposal for Divergence-Free Quantization of Covariant Scalar Fields

TL;DR

This paper introduces a novel divergence-free quantization method for covariant scalar fields, enabling consistent solutions for models previously considered nonrenormalizable, especially in higher spacetime dimensions.

Contribution

It proposes a divergence-free quantization approach based on a pseudofree theory, improving solutions for nonrenormalizable models like ^n in higher dimensions.

Findings

Provides divergence-free solutions for ^n models in n and n.

Enables perturbation analysis about a pseudofree theory, avoiding divergences.

Offers a new approach for quantizing 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., $\phi^4_n$, for spacetime dimension $n\ge4$, but offers a new, divergence-free solution, for less-singular models as well, e.g., $\phi^4_n$, for $n=2,3$.