Phys. Rev. D 62, 085017 (2000) [8 pages]

Character expansions, Itzykson-Zuber integrals, and the QCD partition function

Abstract

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A. B. Balantekin^*,†
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706
Max-Planck-Institut für Kernphysik, Postfach 103980, D-69029 Heidelberg, Germany

Received 8 June 2000; published 26 September 2000

A combinatorial formula to generate U(N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated. Several examples are given, including direct and very quick calculations of the Itzykson-Zuber integral and the finite volume effective partition function of QCD in the sector with a given topological charge.

URL:

http://link.aps.org/doi/10.1103/PhysRevD.62.085017

DOI:

10.1103/PhysRevD.62.085017

PACS:

11.15.Ha, 11.15.Pg

^*Electronic address: baha@nucth.physics.wisc.edu

^†Permanent address.

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Phys. Rev. D 62, 085017 (2000) [8 pages]

Character expansions, Itzykson-Zuber integrals, and the QCD partition function