  A class of non-Dirac-hermitian many-particle quantum systems admitting
entirely real spectra and unitary time-evolution is presented. These quantum
models are isospectral with Dirac-hermitian systems and are exactly solvable.
The general method involves a realization of the basic canonical commutation
relations defining the quantum system in terms of operators those are hermitian
with respect to a pre-determined positive definite metric in the Hilbert space.
Appropriate combinations of these operators result in a large number of
pseudo-hermitian quantum systems admitting entirely real spectra and unitary
time evolution. Examples of a pseudo-hermitian rational Calogero model and XXZ
spin-chain are considered.
