Mathematical Methods of Field Theories

Venerabile Lavagna

The analysis of the structural properties and of the physical models in classical and in quantum field theory, both on Minkowski and on a curved background, requires the use of several, modern mathematical techniques which range from differential geometry to algebra and to functional analysis.

Working in the framework of algebraic quantum field theory, our research interests are rather diversified including for example

  • black hole physics (the Hawking and the anti-Hawking effect, the Unruh-de Witt detectors),
  • the mathematical formulation of gauge theories,
  • the development of models of quantum field theories of manifolds with boundaries,
  • the role of renormalization studied with tools proper of microlocal analysis.

Recently we have also started a thorough investigation of the role of renormalization in complex systems, especially in the solution of stochastic partial differentail equations, using techniques borrowed from quantum field theory.

Contact: Claudio Dappiaggi

Members of the Group: Alberto Bonicelli, Beatrice Costeri, Claudio Dappiaggi e Luca Sinibaldi.