We show how to generate the long-ranged Coulomb interaction with the help of an auxiliary field evolving with constrained but local dynamics. This allows one to simulate systems containing electric charges without ever calculating the Coulomb potential or solving Poisson's equation. Our methods require the imposition of Gauss's law as a dynamical constraint. \par The dynamical system samples a constrained partition function, which leads to a new formulation of Lifshitz/Casimir forces. We show how to evaluate such interactions in complex geometries. \\ \\ \\ (Nota : café à 13h30)