  A Duistermaat-Guillemin-Gutzwiller trace formula for Dirac-type operators on
a globally hyperbolic spatially compact stationary spacetime is achieved by
generalising the recent construction by A. Strohmaier and S. Zelditch [Adv.
Math. \textbf{376}, 107434 (2021)] to a vector bundle setting. We have analysed
the spectrum of the Lie derivative with respect to a global timelike Killing
vector field on the solution space of the Dirac equation and found that it
consists of discrete real eigenvalues. The distributional trace of the time
evolution operator has singularities at the periods of induced Killing flow on
the space of lightlike geodesics. This gives rise to the Weyl law asymptotic at
the vanishing period.
