Pseudo-Hermiticity, $$mathcal{P}mathcal{T}$$ symmetry,and the metric operator

The main achievements of Pseudo-Hermitian Quantum Mechanics and its distinction from the indefinite-metric quantum theories are reviewed. The issue of the non-uniqueness of the metric operator and its consequences for defining the observables are discussed. A systematic perturbative expression for the most general metric operator is offered and its application for a toy model is outlined. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.