Related papers: A BPHZ Theorem in Configuration Space
A configuration space version of BPHZ renormalization is proved in the realm of perturbative algebraic quantum field theory. All arguments are formulated entirely in configuration space so that the range of application is extended to…
A new formalism is given for the renormalization of quantum field theories to all orders of perturbation theory, in which there are manifestly no overlapping divergences. We prove the BPH theorem in this formalism, and show how the local…
We provide a self-contained formulation of the BPHZ theorem in the Euclidean context, which yields a systematic procedure to "renormalise" otherwise divergent integrals appearing in generalised convolutions of functions with a singularity…
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…
We provide a relatively compact proof of the BPHZ theorem for regularity structures of decorated trees in the case where the driving noise satisfies a suitable spectral gap property, as in the Gaussian case. This is inspired by the recent…
We prove a general theorem on the stochastic convergence of appropriately renormalized models arising from nonlinear stochastic PDEs. The theory of regularity structures gives a fairly automated framework for studying these problems but…
Two BPHZ convergence theorems are proved directly in Euclidean position space, without exponentiating the propagators, making use of the Cluster Convergence Theorem presented previously. The first theorem proves the absolute convergence of…
In a recent work a modified BPHZ scheme has been introduced and applied to one-loop Feynman graphs in non-commutative phi^4-theory. In the present paper, we first review the BPHZ method and then we apply the modified BPHZ scheme as well as…
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…
A power-counting theorem is presented, that is designed to play an analogous role, in the proof of a BPHZ convergence theorem, in Euclidean position space, to the role played by Weinberg's power-counting theorem, in Zimmermann's proof of…
The perturbative construction of the S-matrix in the causal spacetime approach of Epstein and Glaser may be interpreted as a method of regularization for divergent Feynman diagrams. The results of any method of regularization must be…
In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…
We give a proof of the convergence of the BHZ renormalized model associated with the generalized (KPZ) equation that does not require the full strength of the BPHZ renormalisation. Our approach is based on a convenient form of chaos…
We show that general cutoff scalar field theories in four dimensions are perturbatively renormalizable through the use of diagrammatic techniques and an adapted BPH renormalization method. Weinberg's convergence theorem is used to show that…
The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic…
Quantum Field Theory, as the keystone of particle physics, has allowed great insights to deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of…
Renormalized perturbation theory \`a la BPHZ can be founded on causality as analyzed by H. Epstein and V. Glaser in the seventies. Here, we list and discuss a number of additional constraints of algebraic character some of which have to be…
We prove the well-posed character of a regularity structure formulation of the quasilinear generalized (KPZ) equation and give an explicit form for a renormalized equation in the full subcritical regime. Under the assumption that the BPHZ…
The description of symmetry breaking proposed by K. Symanzik within the framework of renormalizable theories is generalized from the geometrical point of view. For an arbitrary compact Lie group, a soft breaking of arbitrary covariance, and…
This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate…