dorsal/arxiv
View SchemaOn Explicit Parametrisation of Spectral Curves for Moser-Calogero Particles and its Applications
| Authors | K. L. Vaninsky |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9808018 |
| URL | https://arxiv.org/abs/solv-int/9808018 |
| Journal | Int.Math.Res.Not. 10 (1999) 509-529 |
Abstract
The system of $N$ classical particles on the line with the Weierstrass $\wp$ function as potential is known to be completely integrable. Recently D'Hoker and Phong found a beautiful parameterization by the polynomial of degree $N$ of the space of Riemann surfaces associated with this system. In the trigonometric limit of the elliptic potential these Riemann surfaces degenerate into rational curves. The D'Hoker-Phong polynomial in the limit describes the intersection points of the rational curves. We found an explicit determinant representation of the polynomial in the trigonometric case. We consider applications of this result to the theory of Toeplitz determinants and to geometry of the spectral curves. We also prove our earlier conjecture on the asymptotic behavior of the ratio of two symplectic volumes when the number of particles tends to infinity.
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"abstract": "The system of $N$ classical particles on the line with the Weierstrass $\\wp$\nfunction as potential is known to be completely integrable. Recently D\u0027Hoker\nand Phong found a beautiful parameterization by the polynomial of degree $N$ of\nthe space of Riemann surfaces associated with this system. In the trigonometric\nlimit of the elliptic potential these Riemann surfaces degenerate into rational\ncurves. The D\u0027Hoker-Phong polynomial in the limit describes the intersection\npoints of the rational curves. We found an explicit determinant representation\nof the polynomial in the trigonometric case. We consider applications of this\nresult to the theory of Toeplitz determinants and to geometry of the spectral\ncurves. We also prove our earlier conjecture on the asymptotic behavior of the\nratio of two symplectic volumes when the number of particles tends to infinity.",
"arxiv_id": "solv-int/9808018",
"authors": [
"K. L. Vaninsky"
],
"categories": [
"solv-int",
"hep-ph",
"hep-th",
"nlin.SI"
],
"journal_ref": "Int.Math.Res.Not. 10 (1999) 509-529",
"title": "On Explicit Parametrisation of Spectral Curves for Moser-Calogero Particles and its Applications",
"url": "https://arxiv.org/abs/solv-int/9808018"
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