Invented as a multiscale approach to the theory of critical phenomena, the renormalization group has become a powerful mathematical tool in the analysis of infinite-dimensional systems. Its applications range from classical and quantum statistical mechanics and quantum field theory to partial differential equations, operator theory, and probability theory. Deep connections of renormalization group flows to geometric flows exist.
Cite this article
Margherita Disertori, Joel Feldman, Manfred Salmhofer, The Renormalization Group. Oberwolfach Rep. 8 (2011), no. 1, pp. 781–824DOI 10.4171/OWR/2011/15