Fractional spin through quantum affine algebras

Vyjayanthi Chari, Andrew Pressley

Pedro de M. Rios, Eldar Straume

Hitoshi Konno

Spin generalization of the relativistic Calogero - Sutherland model is constructed by using the affine Hecke algebra and shown to possess the quantum affine symmetry . The spinless model is exactly diagonalized by means of the Macdonald symmetric polynomials. The dynamical density - density correlation function, as well as the one-particle Green function, are evaluated exactly. We also investigate the finite-size scaling of the model and show that the low-energy behaviour is described by the C = 1 Gaussian theory with a new selection rule. The results indicate that the excitations obey the fractional exclusion statistics and also exhibit the Tomonaga - Luttinger liquid behaviour.

Akishi Kato

Mohammed Daoud A, M. Kibler

Two complementary approaches of N = 2 fractional supersymmetric quantum mechanics of order k are studied in this article. The first one, based on a generalized Weyl-Heisenberg algebra W(k) (that comprizes the affine quantum algebra Uq(sl(2)) with q to k = 1 as a special case), apparently contains solely one bosonic degree of freedom. The second one uses generalized bosonic and k-fermionic degrees of freedom. As an illustration, a particular emphasis is put on the fractional supersymmetric oscillator of order k.

L. Frappat, A. Sciarrino, S. Sciuto +1 more