Pseudo-Hermitian Hamiltonians,indefinite inner product spaces and their symmetries

Miloslav Znojil

Ashok Das

In these lectures, we will describe a systematic procedure for constructing an inner product in a pseudo-Hermitian quantum mechanical system.

Mustapha Maamache, Nour El Houda Absi

Alberto Blasi, G. Scolarici, Luigi Solombrino

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 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.

G. Scolarici

A Blasi, G Scolarici, L Solombrino

We extend the definition of generalized parity P , charge-conjugation C and time-reversal T operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and 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 T P and CT P 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.