An analyst's take on the BPHZ theorem

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Title: An analyst's take on the BPHZ theorem
Authors: Hairer, M
Item Type: Working Paper
Abstract: 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 of prescribed order at their origin. We hope that the formulation given in this article will appeal to an analytically minded audience and that it will help to clarify to what extent such renormalisations are arbitrary (or not). In particular, we do not assume any background whatsoever in quantum field theory and we stay away from any discussion of the physical context in which such problems typically arise.
Issue Date: 4-Jul-2018
URI: http://hdl.handle.net/10044/1/64261
Publisher: arXiv
Copyright Statement: © 2018 The Author.
Keywords: math-ph
math-ph
math.CA
math.MP
math-ph
math-ph
math.CA
math.MP
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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