Intrinsic Vertex Regularization and Renormalization in $\phi^4$ Field Theory

TL;DR

This paper introduces a novel regularization and renormalization method in quantum field theory, demonstrated through the one-loop renormalization of $$ theory, leveraging the intrinsic relations between divergent and convergent functions.

Contribution

It proposes a new approach to regularization and renormalization based on intrinsic relations in QFT, applied to $$ theory at one loop.

Findings

Successfully renormalized $$ theory at one loop using the new method.

Established a link between divergent and convergent functions in renormalizable QFTs.

Demonstrated the effectiveness of the method in a standard quantum field theory example.

Abstract

Based upon the intrinsic relation between the divergent lower point functions and the convergent higher point ones in the renormalizable quantum field theories, we propose a new method for regularization and renormalization in QFT. As an example, we renormalize the $\phi^{4}$ theory at the one loop order by means of this method.