Normal Products and Zimmermann Identities in Configuration Space BPHZ Renormalization
arXiv:1708.04115
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.
33 pages, v2: preliminaries extended, notation unified, figures added
References in corpus (8)
- Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
- Exponential renormalization
- The operator product expansion for perturbative quantum field theory in curved spacetime
- Dimensional Regularization in Position Space and a Forest Formula for Regularized Epstein-Glaser Renormalization
- Configuration Space BPHZ Renormalization on Analytic Spacetimes
- Renormalization of Feynman amplitudes on manifolds by spectral zeta regularization and blow-ups
- A BPHZ Theorem in Configuration Space
- BPHZ Renormalization in Configuration Space for the -Model