Jürg Fröhlich

TL;DR: The study of phase transitions and the approach to critical points in physical systems in thermal equilibrium is an important part of equilibrium statistical mechanics, but its significance goes beyond statistical physics proper: it is crucial for condensed matter physics and for relativistic quantum field theory as mentioned in this paper.

TL;DR: In this article, the convergence of the grand-canonical equilibrium states of Bose gases to their mean-field limits is studied, which are given by the Gibbs measures of classical field theories with quartic Hartree-type self-interaction.

TL;DR: In this article, it was shown that a principal bundle with connection can be characterized uniquely by its Wilson loops, and the quantization of the Wilson loops is based on converting them into random fields on a manifold of oriented loops, a problem in random geometry.

TL;DR: In this paper, the authors studied the stationary states of a quantum mechanical system describing an atom coupled to black-body radiation at positive temperature, and they showed that if Fermi's Golden Rule predicts that a stationary state disintegrates after coupling to the radiation field then it is unstable, provided the coupling constant is sufficiently small (depending on the temperature).

TL;DR: The coset construction is the most important tool to construct rational conformal field theories with known chiral data as discussed by the authors, and for some cosets at small level, so-called maverick cosets, the familiar analysis using selection and identification rules breaks down.