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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2003

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

Résumé

The integral over the U(N) unitary group $I=\int DU \exp\Tr A U B U^\dagger$ is reexamined. 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 on what they teach us on the large $N$ limit of $\log I$.

Dates et versions

hal-00002260 , version 1 (28-01-2005)

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Paul Zinn-Justin, Jean-Bernard Zuber. On some integrals over the U(N) unitary group and their large N limit. Journal of Physics A: Mathematical and Theoretical, 2003, 36, pp.3173-3194. ⟨hal-00002260⟩
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