Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory

Details Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory

2004-07-12

arxiv.org/abs/math-ph/0407021v2

J.Phys. A37 (2004) 11379-11390

Physics

Mathematical Physics

12 pages, 1 figure, amslatex, bibtex (added missing label eq.11)

Scientific paper

10.1088/0305-4470/37/47/007

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; these can be associated to Riemannian symmetric spaces of rank one with positive, negative or vanishing curvature. For all other cases an accurate semiclassical approximation is derived, based on the identification of the operators with a peculiar Schroedinger-like operator.

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