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

Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation