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Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras | | E. D’Hoker
; D.H. Phong
; | | Date: |
19 Apr 1998 | | Journal: | Nucl.Phys. B530 (1998) 611-640 | | Subject: | High Energy Physics - Theory; Exactly Solvable and Integrable Systems | hep-th nlin.SI solv-int | | Abstract: | The elliptic Calogero-Moser Hamiltonian and Lax pair associated with a general simple Lie algebra $G$ are shown to scale to the (affine) Toda Hamiltonian and Lax pair. The limit consists in taking the elliptic modulus $ au$ and the Calogero-Moser couplings $m$ to infinity, while keeping fixed the combination $M = m e^{i pi delta au}$ for some exponent $delta$. Critical scaling limits arise when $1/delta$ equals the Coxeter number or the dual Coxeter number for the untwisted and twisted Calogero-Moser systems respectively; the limit consists then of the Toda system for the affine Lie algebras $G^{(1)}$ and $(^{(1)})^vee$. The limits of the untwisted or twisted Calogero-Moser system, for $delta$ less than these critical values, but non-zero, consists of the ordinary Toda system, while for $delta =0$, it consists of the trigonometric Calogero-Moser systems for the algebras $G$ and $G^vee$ respectively. | | Source: | arXiv, hep-th/9804125 | | Services: | Forum | Review | PDF | Favorites | |
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