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We consider the one-dimensional Dirac equation for the harmonic oscillatorand the associated second order separated operators giving the resonances ofthe problem by complex dilation. The same operators have unique extensions asclosed PT-symmetric operators defining infinite positive energy levelsconverging to the Schroedinger ones as c tends to infinity. Such energy levelsand their eigenfunctions give directly a definite choice of metastable statesof the problem. Precise numerical computations shows that these levels coincidewith the positions of the resonances up to the order of the width. Similarresults are found for the Klein-Gordon oscillators, and in this case there isan infinite number of dynamics and the eigenvalues and eigenvectors of thePT-symmetric operators give metastable states for each dynamics.

PT-symmetric operators and metastable states of the 1D relativistic oscillators