BPHZ Renormalization in Configuration Space for the $\mathcal{A}^4$-Model

TL;DR

This paper reviews recent BPHZ renormalization techniques in configuration space and applies them to a scalar quantum field with quartic interaction, extending key results and analyzing the equation of motion.

Contribution

It extends BPHZ renormalization results to a quadratic normal product and explores the equation of motion in the -model within configuration space.

Findings

Extended short-distance expansion for quadratic normal products.

Derived the Zimmermann identity for the -model.

Computed the interacting field's equation of motion.

Abstract

Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.