  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\"{o}dinger
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.
