In this context I will argue that there is a class of detector models in which nonperturbative, local and covariant, as well as mathematically tractable results can be achieved.

Our approach combines several features of other models encountered in the literature of relativistic quantum information, namely scattering processes, quantum Brownian motion models, and Gaussian dynamics. I will argue that,  in order to model nontrivial, yet simple processes respecting causality and covariance, pointlike, ill-defined interactions are necessary, but these can be renormalized consistently a la Epstein Glasser. I will further analyze the model in the context of quantum measurement theory and argue that these models generate well-defined induced observables.

Our formalism can be used to detect non-Gaussianities present in the field's state in a local and covariant way, and the nonperturbative nature of the problem provides an operational framework to discuss Bell inequalities in quantum field theory. Based on arXiv:2502.01283.