A BPHZ Theorem in Configuration Space

Abstract

The concept of BPHZ renormalization is translated into configuration space. After deriving the counterpart for the regularizing Taylor subtraction, a new version of Zimmermann's convergence theorem by means of the forest formula is proved. Furthermore, a sufficient condition on the algebraic decay of the integrand is formulated such that the constant coupling limit exists in the new setting.

21 pages, v3: minor clarifications

References in corpus (2)

• An analytic BPHZ theorem for regularity structures
• Configuration Space BPHZ Renormalization on Analytic Spacetimes

Cited by in corpus (3)

• Configuration Space BPHZ Renormalization on Analytic Spacetimes
• BPHZ Renormalization in Configuration Space for the ${\mathcal{A}}^4$-Model
• Normal Products and Zimmermann Identities in Configuration Space BPHZ Renormalization