An Itzykson–Zuber-like integral and diffusion for complex ordinary and supermatrices

1996/05/31 by Thomas Guhr, Tilo Wettig · 72 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Complex system #Diffusion #Diffusion equation #Field (mathematics) #Fractional Differential Equations Solutions #Integral equation #Noncommutative and Quantum Gravity Theories #Quantum #Quantum field theory #Space (punctuation) #hep-th

paper · pdf · doi:10.1063/1.531784

published in Journal of Mathematical Physics 37(12), 6395-6413 (American Institute of Physics) · 20 pages, RevTeX, no figures, agrees with published version, including "Note added in proof" with an additional result for rectangular supermatrices

openalex publication_date 1996/12/01 · arxiv created 2014/10/08 · arxiv updated 2014/10/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We compute an analogue of the Itzykson–Zuber integral for the case of arbitrary complex matrices. The calculation is done for both ordinary and supermatrices by transferring the Itzykson–Zuber diffusion equation method to the space of arbitrary complex matrices. The integral is of interest for applications in quantum chromodynamics and the theory of two-dimensional quantum gravity.

Citations

• Correlation functions in the Itzykson-Zuber model
• Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit
• Integration on noncompact supermanifolds
• Spherical Functions on a Semisimple Lie Group, I

Cited by

• GUE-chGUE transition preserving chirality at finite matrix size