QuasiHermitian supersymmetric extensions of a nonHermitian oscillator Hamiltonian and of its generalizations
Abstract
A harmonic oscillator Hamiltonian augmented by a nonHermitian {\cal PT} symmetric part and its su(1,1) generalizations, for which a family of positivedefinite metric operators was recently constructed, are reexamined in a supersymmetric context. Some quasiHermitian supersymmetric extensions of such Hamiltonians are proposed by enlarging su(1,1) to a su(1,1/1) \sim osp(2/2, {\bb R}) superalgebra. This allows the construction of new nonHermitian Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2008
 DOI:
 10.1088/17518113/41/24/244022
 arXiv:
 arXiv:0710.2453
 Bibcode:
 2008JPhA...41x4022Q
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 15 pages, no figure