  We study the one-dimensional Dirac equation with local PT-symmetric
potentials whose discrete eigenfunctions and continuum asymptotic
eigenfunctions are eigenfunctions of the PT operator, too: on these conditions
the bound-state spectra are real and the potentials are reflectionless and
conserve unitarity in the scattering process. Absence of reflection makes it
meaningful to consider also PT-symmetric potentials that do not vanish
asymptotically.
