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

arXiv comment18 pages; submitted to Nuclear Physics B

References in corpus (6)

• Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Configuration Space BPHZ Renormalization on Analytic Spacetimes
• A BPHZ Theorem in Configuration Space
• Conformal transformations of the S-matrix; $\beta$-function identifies change of spacetime
• Normal Products and Zimmermann Identities in Configuration Space BPHZ Renormalization

Cited by in corpus (2)

• Dimensional regularization, Wilsonian RG, and the Naturalness/Hierarchy problem
• Normal Products and Zimmermann Identities in Configuration Space BPHZ Renormalization