Renormalization theory based on flow equations

Christoph Kopper

doi:10.1007/978-3-7643-7434-1_12

Renormalization theory based on flow equations

Christoph Kopper

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

7 Citations (Scopus)

Abstract

I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson renormalization group. I first consider massive Euclidean φ⁴₄ -theory. The renormalization proofs are achieved through inductive bounds on regularized Schwinger functions. I present relatively crude bounds which are easily proven, and sharpened versions (which seem to be optimal as regards large momentum behaviour). Then renormalizability statements in Minkowski space are presented together with analyticity properties of the Schwinger functions. Finally I give a short description of further results.

Original language	English
Title of host publication	Progress in Mathematics
Publisher	Springer Basel
Pages	161-174
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-7643-7434-1_12
Publication status	Published - 1 Jan 2007

Publication series

Name	Progress in Mathematics
Volume	251
ISSN (Print)	0743-1643
ISSN (Electronic)	2296-505X

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10.1007/978-3-7643-7434-1_12

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AB - I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson renormalization group. I first consider massive Euclidean φ44 -theory. The renormalization proofs are achieved through inductive bounds on regularized Schwinger functions. I present relatively crude bounds which are easily proven, and sharpened versions (which seem to be optimal as regards large momentum behaviour). Then renormalizability statements in Minkowski space are presented together with analyticity properties of the Schwinger functions. Finally I give a short description of further results.

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Renormalization theory based on flow equations

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