Quantization of Non-Polynomial Field Theories

TL;DR

This paper develops a new method for quantizing a class of non-polynomial scalar field theories, bridging free and $4$ theories, and provides tools to analyze their correlation functions and triviality.

Contribution

It introduces a novel approach to quantize non-polynomial scalar theories and derives Feynman rules to study their properties, aiding understanding of $4$ triviality.

Findings

New Feynman rules for non-polynomial theories

Correlation functions can be calculated using the proposed method

Progress towards understanding $4$ triviality in four dimensions

Abstract

We re-examine the quantization of a class of non-polynomial scalar field theories which interpolates continuously from a free one to $\phi^4$ theory. The quantization of such theories is problematic because the Feynman rules may not be directly obtained. We give a means for calculating the correlation functions in this theory. The Feynman rules developed here shall enable further progress in the understanding of the triviality of $\phi^4$ theory in four dimensions.