T. R. (Tom) Hurd

Professor of Mathematics

Construction of models in quantum field theory

The functional integral in quantum field theory (QFT) and its analogue the partition function in statistical physics are used to give unified, concise, but usually only heuristic, characterizations of elementary particle and condensed matter physics models and their symmetries. The Brydges-Yau-Dimock-Hurd constructive method is one coherent rigorous and mathematical approach to understanding functional integrals. In ten years of development, it has been applied to numerous fundamental problems in QFT and statistical physics, many of which have never been rigorously treated by other means: the dipole gas, the Coulomb gas, sine--Gordon QFT, quantum electrodynamics, the phi^4_d model in dimensions d=3 and d=4-epsilon. I am currently working on such problems as correlation functions, the construction of a jointly long-distance/short-distance convergent massless model, and the construction of the Coulomb gas at the famous Kosterlitz-Thouless transition point.

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last updated  25/10/00