Integration of Grassmann variables over invariant functions on flat superspaces

DOI10.1063/1.3049630zbMath1200.58008arXiv0809.2674OpenAlexW3100742999MaRDI QIDQ3650897

Thomas Guhr, Mario Kieburg, Heiner Kohler

Publication date: 7 December 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.2674

zbMATH Keywords

Cauchy-like integral theorems for invariant functions on supervectorsderivation of supermatrix Bessel-functionsflat superspacesintegration of Grassmann variablessymmetric supermatrices

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Groups and algebras in quantum theory (81R99) Analysis on supermanifolds or graded manifolds (58C50) Exterior algebra, Grassmann algebras (15A75)

Related Items (6)

The correlated Jacobi and the correlated Cauchy-Lorentz ensembles ⋮ Random matrices with row constraints and eigenvalue distributions of graph Laplacians ⋮ Berezin integral as a limit of Riemann sum ⋮ Orthosymplectically invariant functions in superspace ⋮ Local tail statistics of heavy-tailed random matrix ensembles with unitary invariance ⋮ Asymptotic coincidence of the statistics for degenerate and non-degenerate correlated real Wishart ensembles

Cites Work

• Equivalence of QCD in the \(\epsilon\)-regime and chiral random matrix theory with or without chemical potential
• Fourier analysis on a hyperbolic supermanifold with constant curvature
• Transitions toward quantum chaos: with supersymmetry from Poisson to Gauss
• Gelfand-Tsetlin coordinates for the unitary supergroup
• The supersymmetric transfer matrix for linear chains with nondiagonal disorder.
• Superbosonization formula and its application to random matrix theory
• Superbosonization of invariant random matrix ensembles
• Spherical Functions on a Semisimple Lie Group, I
• Dyson’s correlation functions and graded symmetry
• Arbitrary unitarily invariant random matrix ensembles and supersymmetry
• Universality of level correlation function of sparse random matrices
• Fourier–Bessel analysis for ordinary and graded 2×2 Hermitian matrices
• Supersymmetry in Disorder and Chaos
• New correlation functions for random matrices and integrals over supergroups
• Thek-point random matrix kernels obtained from one-point supermatrix models
• The integral theorem for supersymmetric invariants
• The planar approximation. II
• Recursive construction for a class of radial functions. I. Ordinary space
• Recursive construction for a class of radial functions. II. Superspace
• Riemannian symmetric superspaces and their origin in random-matrix theory
• Supersymmetric extensions of Calogero–Moser–Sutherland-like models: construction and some solutions

This page was built for publication: Integration of Grassmann variables over invariant functions on flat superspaces