Quantum Point Charges Interacting with Quasi-classical Electromagnetic Fields

We study effective models describing systems of quantum particles interacting with quantized (electromagnetic) fields in the quasi-classical regime, i. e. , when the field's state shows a large average number of excitations. Once the field's degrees of freedom are traced out on factorized states, the reduced dynamics of the particles' system is described by an effective Schr\"odinger operator keeping track of the field's state. We prove that, under suitable assumptions on the latter, such effective models are well-posed even if the particles are point-like, that is no ultraviolet cut-off is imposed on the interaction with quantum fields.