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

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

2002-09-10

arxiv.org/abs/math-ph/0209019v3

J.Phys.A36:3173-3194,2003

Physics

Mathematical Physics

revised: comment added in sec. 3.2

Scientific paper

10.1088/0305-4470/36/12/318

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 $\log I$.

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