A SUSY formulation a la Witten for the SUSY isotonic oscillator canonical supercoherent states

Citation
J. Jayaraman et al., A SUSY formulation a la Witten for the SUSY isotonic oscillator canonical supercoherent states, J PHYS A, 32(38), 1999, pp. 6643-6652
Citations number
42
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
32
Issue
38
Year of publication
1999
Pages
6643 - 6652
Database
ISI
SICI code
0305-4470(19990924)32:38<6643:ASFALW>2.0.ZU;2-8
Abstract
We extend Witten's supersymmetry (SUSY) formulation for Hamiltonian systems to a system of annihilation operator eigenvalue equations associated with the SUSY isotonic oscillator, which, as we show, define SUSY canonical supe rcoherent states containing mixtures of both pure bosonic and pure fermioni c counterparts. Specifically, a graded Lie algebra structure analogous to W itten's SUSY quantum mechanical algebra is realized in which only annihilat ion operators participate, all expressed in terms of the Wigner annihilatio n operator of a related super-Wigner oscillator system.