Unlabeled long range interacting particle systems with jumps (dynamical systems on the configuration space) were constructed by Esaki[Tohoku J, 2019] using Dirichlet form technique. In this talk, we would like to give infinite dimensional stochastic differential equation (ISDE) representations for each particle on the dynamics. We assume some conditions to show our theorem. We call them non-collision, non-explosion and no-big jump conditions. In this talk, we give sufficient conditions for these conditions. Using these sufficient condition we can apply our theorem to the systems of alpha-stable particles with logarithmic interactions associated with Dyson, Ginibre, Airy and Bessel random point fields, which are related to the random matrix theory. This is a joint work with Hideki Tanemura (Keio University).