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arXiv · hep-th/9506105

Exact Solvability of the Calogero and Sutherland Models

Werner Ruhl·Alexander Turbiner
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Abstract

Translationally invariant symmetric polynomials as coordinates for $N$-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland $N$-body Hamiltonians, after appropriate gauge transformations, can be presented as a {\it quadratic} polynomial in the generators of the algebra $sl_N$ in finite-dimensional degenerate representation. The exact solvability of these models follows from the existence of the infinite flag of such representation spaces, preserved by the above Hamiltonians. A connection with Jack polynomials is discussed.

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Werner Ruhl, Alexander Turbiner. 1995-08-03. Exact Solvability of the Calogero and Sutherland Models. https://doi.org/10.1142/s0217732395002374

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