PseudoHermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a nonHermitian Hamiltonian
Abstract
We introduce the notion of pseudoHermiticity and show that every Hamiltonian with a real spectrum is pseudoHermitian. We point out that all the PTsymmetric nonHermitian Hamiltonians studied in the literature belong to the class of pseudoHermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudoHermiticity. We explore the basic properties of general pseudoHermitian Hamiltonians, develop pseudosupersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the twocomponent WheelerDeWitt equation for the FRWmodels coupled to a real massive scalar field and a class of pseudoHermitian Hamiltonians with a real spectrum.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 January 2002
 DOI:
 10.1063/1.1418246
 arXiv:
 arXiv:mathph/0107001
 Bibcode:
 2002JMP....43..205M
 Keywords:

 11.30.Er;
 98.80.Hw;
 95.30.Sf;
 04.20.q;
 11.30.Pb;
 11.10.Ef;
 Charge conjugation parity time reversal and other discrete symmetries;
 Relativity and gravitation;
 Classical general relativity;
 Supersymmetry;
 Lagrangian and Hamiltonian approach;
 Mathematical Physics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 Revised version, to appear in J. Math. Phys