Open system dynamics from fundamental Lagrangian

The effective dynamics of a non-relativistic charged particle, interacting with a bath of thermal photons, has been derived using a variety of methods and certain simplifying assumptions. It is therefore desirable to verify if similar conclusions can be reached following a microscopic derivation starting from the QED Lagrangian. In doing so, one may pick between two Lagrangians. One in which the interaction term involves the position of the electron; the other in which it involves the momentum. Since the two Lagrangians differ by a total derivative, one might assume such a choice to be inconsequential. However, it will be shown in this talk that two Lagrangians differing by a total derivative may lead to very different predictions at the level of open quantum systems. Further, it will be argued why only one of the two Lagrangians leads to phenomenologically consistent predictions. One might find these conclusions to be relevant in attempting a microscopic derivation of the effective system dynamics in a variety of situations.