JournalsowrVol. 8 / No. 1DOI 10.4171/owr/2011/15

The Renormalization Group

  • Margherita Disertori

    Rheinische Friedrich-Wilhelms-Universität Bonn, Germany
  • Joel Feldman

    University of British Columbia, Vancouver, Canada
  • Manfred Salmhofer

    Universität Heidelberg, Germany
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Abstract

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.