Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

Simple item page
dc.creatorFerrer, A. Prats
dc.creatorEynard, B.
dc.creatorDi Francesco, P.
dc.creatorZuber, J. -B.
dc.date2006-10-20
dc.date2008-02-25
dc.date.accessioned2026-07-07T11:28:12Z
dc.date.available2026-07-07T11:28:12Z
dc.descriptionThe Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials prod tr{X^{p_1} Omega Y^{q_1} Omega^dagger X^{p_2} ... with the weight exp tr{X Omega Y Omega^dagger} are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat-Heckman's theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions.
dc.description58 pages; Acknowledgements added; small corrections in appendix A; minor changes & Note Added
dc.identifierhttps://arxiv.org/abs/math-ph/0610049
dc.identifierhttp://arxiv.org/abs/math-ph/0610049
dc.identifierJ.Stat.Phys.129:885-935,2009
dc.identifierdoi:10.1007/s10955-007-9350-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/196368
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subject15A52,15A57
dc.titleCorrelation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups
dc.typetext

Files

Collections

arXiv