Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-04-19
Nucl.Phys. B530 (1998) 611-640
Physics
High Energy Physics
High Energy Physics - Theory
34 pages, Plain TeX, minor typos corrected
Scientific paper
10.1016/S0550-3213(98)00569-0
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 $\tau$ and the Calogero-Moser couplings $m$ to infinity, while keeping fixed the combination $M = m e^{i \pi \delta \tau}$ 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 $(\G ^{(1)})^\vee$. 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.
D'Hoker Eric
Phong Duong Hong
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