Superlax pairs and infinite symmetries in the 1/r**2 system

Dec, 1992
10 pages
Published in:
  • Phys.Rev.Lett. 70 (1993) 4029-4033
e-Print:
Report number:
  • PRINT-93-0015

Citations per year

1993200120092017202301234
Abstract: (arXiv)
We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the 1/r 21/r~2 family of interactions. The algebra consists of the commutation between a ``Super- Hamiltonian'', and two other operators, in a Hilbert space that is an enlargement of the original one by introducing fermions. The commutation relations reduce to quantal Ordered Lax equations when projected to the original subspace, and to a statement about the ``Harmonic Lattice Potential'' structure of the Lax operator. These in turn lead to a highly automatic proof of the integrability of these models. In the case of the discrete SU(n)1/r 2SU(n)-1/r~2 model, the `` Super-Hamiltonian'' is again an SU(m)1/r 2SU(m)-1/r~2 model with a related mm, providing an interesting hierarchy of models.