| A method to construct non-Dirac-hermitian supersymmetric quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving both bosonic and fermionic degrees of freedom in terms of non-Dirac-hermitian operators which are hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. In addition to the construction of a general non-Dirac-hermitian supersymmetric quantum system, a few examples including one dimensional shape-invariant potentials, super-conformal quantum system and supersymmetric Calogero-type models admitting entirely real spectra are presented. A connection between pseudo-hermitian matrix model and non-Dirac-hermitian Calogero-type models is also explored. |
|