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Renormalization theory based on flow equations. (English) Zbl 1166.81350
Boutet de Monvel, Anne (ed.) et al., Rigorous quantum field theory. A Festschrift for Jacques Bros. Basel: Birkhäuser (ISBN 3-7643-7433-0/hbk). Progress in Mathematics 251, 161-174 (2007).
Summary: 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 $$\varphi_4^4$$-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.
For the entire collection see [Zbl 1106.00006].

##### MSC:
 81T17 Renormalization group methods applied to problems in quantum field theory 81-02 Research exposition (monographs, survey articles) pertaining to quantum theory 81T08 Constructive quantum field theory 81T10 Model quantum field theories