On some integrals over the U(N) unitary group and their large N limit

Authors: Zinn-Justin P.1; Zuber J-B.2

Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 3173-3193(21)

Publisher: Institute of Physics Publishing

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Abstract:

The integral over the U(N) unitary group I DU exp Tr AUBU is re-examined. Various approaches and extensions are first reviewed. The second half of the paper deals with more recent developments: relation with integrable Toda lattice hierarchy, diagrammatic expansion and combinatorics, and what they teach us on the large N limit of log I.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, Bâtiment 100, F-91405 Orsay Cedex, France 2: Service de Physique Théorique de Saclay, CEA/DSM/SPhT, Unité de recherche associée au CNRS, CEA-Saclay, F-91191 Gif sur Yvette Cedex, France

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