We establish orthonormal Strichartz estimates for the fractional Schrödinger equations on torus and waveguide manifold. In the process, we also improve ² decoupling inequality and establish classical fractional Strichartz estimates on waveguide manifold. This maybe of independent interest. As an application, we establish local well-posednes for the Hartree equations with infinitely many particles with non-trace class initial data.
Bhimani et al. (2025) studied this question.