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

P. Zinn-Justin; J. -B. Zuber

doi:10.1088/0305-4470/36/12/318

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

Mathematical Physics 2009-09-29 v3 Condensed Matter High Energy Physics - Theory Combinatorics math.MP

Authors: P. Zinn-Justin , J. -B. Zuber

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

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 $\log I$ .

Keywords

unitary group integral large n limit toda lattice diagrammatic expansion combinatorics u(n)

Cite

@article{arxiv.math-ph/0209019,
  title  = {On some integrals over the U(N) unitary group and their large N limit},
  author = {P. Zinn-Justin and J. -B. Zuber},
  journal= {arXiv preprint arXiv:math-ph/0209019},
  year   = {2009}
}

Comments

revised: comment added in sec. 3.2

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

Abstract

Keywords

Cite

Comments

Related papers