Normal Products and Zimmermann Identities in Configuration Space BPHZ Renormalization

TL;DR

This paper develops a configuration space BPHZ renormalization framework using normal products, extending Wick products, and introduces Zimmermann identities to relate different subtraction degrees, with applications to wave operators.

Contribution

It introduces a new formulation of normal products in configuration space BPHZ renormalization and derives Zimmermann identities within this setting.

Findings

Normal products allow the limit of coinciding field operators.

Zimmermann identities relate field monomials with different subtraction degrees.

Wave operators' action on elementary fields is explicitly calculated.

Abstract

The notion of normal products, a generalization of Wick products, is derived with respect to BPHZ renormalization formulated entirely in configuration space. Inserted into time-ordered products, normal products admit the limit of coinciding field operators, which constitute the product. The derivation requires the introduction of Zimmermann identities, which relate field monomials or renormalization parts with differing subtraction degree. Furthermore, we calculate the action of wave operators on elementary fields inserted into time-ordered products, exploiting the properties of normal products.