  In this paper we prove the orthonormal Strichartz estimates for the higher
order and fractional Schr\"odinger, wave, Klein-Gordon and Dirac equations with
potentials. As in the case of the Schr\"odinger operator, the proofs are based
on the smooth perturbation theory by T. Kato. However, for the Klein-Gordon and
Dirac equations, we also use a method of the microlocal analysis in order to
prove the estimates for wider range of admissible pairs. As applications we
prove the global existence of a solution to the higher order or fractional
Hartree equation with potentials which describes the dynamics of infinitely
many particles. We also give a local existence result for the semi-relativistic
Hartree equation with electromagnetic potentials. As another application, the
refined Strichartz estimates are proved for higher order and fractional
Schr\"odinger, wave and Klein-Gordon equations.
