ar X iv : q ua nt - p h / 03 10 10 6 v 2 2 7 Fe b 20 04 Pseudo - Hermitian Hamiltonians , indefinite inner product spaces and their symmetries ∗

Abstract

We extend the definition of generalized parity P , charge-conjugation C and time-reversal T operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and we use these generalized operators to describe the full set of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold classification. In particular we show that TP and CTP are the generators of the P -antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian H to admit a P -reflecting symmetry which generates the P -pseudounitary and the P pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the P -unitary evolution of a physical system are also given. PACS: 11.30.Er; 03.65.Ca; 03.65.Fd

Cite this paper

@inproceedings{Blasi2008arXI, title={ar X iv : q ua nt - p h / 03 10 10 6 v 2 2 7 Fe b 20 04 Pseudo - Hermitian Hamiltonians , indefinite inner product spaces and their symmetries ∗}, author={Alexandre Blasi and G . Scolarici and L . Solombrino}, year={2008} }