Integration formulas and exact calculations in the Calogero-Sutherland model

Abstract

Some integration formulas which either occur or are implicit in Ha's recent exact calculation of some correlations in the Calogero-Sutherland model are discussed. These integration formulas include the calculation of the inner product $<0|\rho (0)|\kappa >$ between the density operator acting on an excited state and the ground state, and a generalization of the Selberg integral due to Dotsenko and Fateev.

12 pgs (one fig. not included), latex, some corrections made before publication in Lett. Mod. Phys. B

References in corpus (2)

• Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
• Towards exact bosonization of the Calogero-Sutherland model

Cited by in corpus (11)

• Finite N Fluctuation Formulas for Random Matrices
• Integral Representations of the Macdonald Symmetric Functions
• Singularity dominated strong fluctuations for some random matrix averages
• Correlations for the Dyson Brownian motion model with Poisson initial conditions
• Elementary Excitations and Dynamical Correlation Functions of the Calogero-Sutherland Model with Internal Symmetry
• Hellmann-Feynman theorem and fluctuation-correlation analysis of the Calogero-Sutherland model
• On a Selberg-Schur integral
• Applications of the Dotsenko-Fateev Integral in Random-Matrix Models
• Generalized weight functions and the Macdonald polynomials
• Parametric Ward-Takahashi identity in disordered systems and the integral identity associated with the Calogero-Sutherland model
• Exact diagonalisation of 1-d interacting spinless Fermions