%0 Journal Article
%T Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
%A Omar Cherbal
%A Mahrez Drir
%A Mustapha Maamache
%A Dimitar A. Trifonov
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2010
%I National Academy of Science of Ukraine
%X A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form H=¦ØJ_3+¦ÁJ_ +¦ÂJ_+, ¦Á¡Ù¦Â, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.
%K pseudo-Hermitian quantum mechanics
%K supersymmetry
%K supercoherent states
%U http://dx.doi.org/10.3842/SIGMA.2010.096