BPHZ renormalization in configuration space for the A4-model

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.

Normal Products and Zimmermann Identities in Configuration Space BPHZ Renormalization

“…It is evident that an analogous argument holds for normal products. For an explicit example, we refer again to [Pot18]. The Zimmermann identity should certainly be used in the aforementioned studies of concrete theories, relating insertion of differing engineering dimension, and the definition of normal products should be of benefit in the study of operator product expansion [Abd16], possibly on analytic spacetimes [Hol07].…”

“…Certainly, the definition will hold only for a single but arbitrary correlation function. For an example of a normal product defined for a perturbative treatment of a theory with one scalar field and quartic self-interaction, we refer to [Pot18].…”

“…The existence of the extended distribution Ru[Γ] is just a consequence of the BPHZ renormalization scheme. [Pot18]…”