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At coupling strengths lambda = 1/2, 1, or 2, the Calogero-Sutherland model(CSM) is related to Brownian motion in a Wigner-Dyson random matrix ensemblewith orthogonal, unitary, or symplectic symmetry. Using this relation inconjunction with superanalytic techniques developed in mesoscopic conductorphysics, we derive an exact integral representation for the CSM two-particleGreen's function in the thermodynamic limit. Simple closed expressions for thesingle-particle Green's functions are extracted by separation of points. Forthe advanced part, where a particle is added to the ground state and laterremoved, a sum of two contributions is found: the expected one with just oneparticle excitation present, plus an extra term arising from fractionalizationof the single particle into a number of elementary particle and holeexcitations.Comment: 19 REVTeX page

Single-particle Green’s functions of the Calogero-Sutherland model at couplings λ=1/2, 1, and 2