Orthonormal Strichartz estimates for Schrödinger operator and their applications to infinitely many particle systems

We develop an abstract perturbation theory for the orthonormal Strichartz estimates, which were first studied by Frank–Lewin–Lieb–Seiringer. The method used in the proof is based on the duality principle by Frank–Sabin and Kato’s smooth perturbation theory. Then we apply it to the magnetic Schrödinger operator or the Schrödinger operator with potentials with critical singularities. We also deduce the refined Strichartz estimates for the Schrödinger operator in terms of the Besov space. In the process of their proofs, some estimates associated with the Besov space or the Triebel-Lizorkin space defined by the Schrödinger operator are deduced. Finally we prove the global existence of a solution for the Hartree equation with electromagnetic potentials describing the dynamics of infinitely many fermions. This would be the first result on the orthonormal Strichartz estimates for the Schrödinger operator with general time-independent potentials including very short range and inverse square type potentials.