Abstract
We investigate the feasibility of performing quantum non-demolition (QND) measurements in relativistic quantum systems, using the one-dimensional Dirac oscillator as a specific example. We derive general expressions for its QND observables and find that they are intricate combinations of the position, momentum, and spin operators, which makes them challenging to realize experimentally in general. However, the situation is considerably simplified in both the weakly and strongly relativistic limits, where their experimental realization will be possible.