On a parastatistical hydrogen atom and its supersymmetric properties

S. N. Biswas, S. K. Soni

The algebraic structure of parastatistics has been generalized and it is found to be consistent with supersymmetric quantum mechanics with supercharges constructed out of the generalized para-Bose and para-Fermi operators. It is further shown that the operator algebra of generalized parastatistics offers a realization of the (graded) orthosymplectic group similar to that of orthogonal and symplectic groups using conventional parastatistics.

Francesco Toppan

Abstract The recent surge of interest in Z 2 × Z 2 -graded invariant mechanics poses the challenge of understanding the physical consequences of a Z 2 × Z 2 -graded symmetry. In this paper it is shown that non-trivial physics can be detected in the multiparticle sector of a theory, being induced by the Z 2 × Z 2 -graded parastatistics obeyed by the particles. The toy model of the N = 4 supersymmetric/ Z 2 × Z 2 -graded oscillator is used. In this set-up the one-particle energy levels and their degenerations are the same for both supersymmetric and Z 2 × Z 2 -graded versions. Nevertheless, in the multiparticle sector, a measurement of an observable operator on suitable states can discriminate whether the system under consideration is composed by ordinary bosons/fermions or by Z 2 × Z 2 -graded particles. Therefore, Z 2 × Z 2 -graded mechanics has experimentally testable consequences. Furthermore, the Z 2 × Z 2

Barry A. Freedman

J. Beckers, N. Debergh

Coherent states are constructed in p=2-parasupersymmetric quantum mechanics in connection with the two relative para-Bose and para-Fermi sets of trilinear structure relations. They are called parasupercoherent states. Parasupersymmetric operators [such as the Hamiltonian and (two) annihilation operators] are introduced and discussed. In particular, the parasuperspectrum is determined and compared with the recent results obtained by Rubakov and Spiridonov [Mod. Phys. Lett. A 3, 1337 (1988)]. The superalgebra contents subtended by osp(2/2) and osp(3/2) are analyzed and exploited in order to get constants of motion in both contexts through parallel properties on the supersymmetric harmonic oscillator.

M. Kibler, Mohammed Daoud A