Action for reaction in general dimension

Abstract

We present an effective field theory study of radiation and radiation reaction effects for scalar and electromagnetic fields in general spacetime dimensions. Our method unifies the treatment of outgoing radiation and its reaction force within a single action principle. Central ingredients are the field doubling method, which is the classical version of the closed time path formalism and allows a treatment of nonconservative effects within an action, action level matching of system and radiation zones, and the use of fields which are adapted to the enhanced symmetries of each zone. New results include compact expressions for radiative multipoles, radiation, and radiation reaction effective action in any spacetime dimension. We emphasize dimension-dependent features such as the difference between electric and magnetic multipoles in higher dimensions and the temporal nonlocality nature of the effective action for odd spacetime dimensions, which is a reflection of indirect propagation (``tail effect'') in the full theory. This work generalizes the method and results developed for four dimensions in Phys. Rev. D 88, 104037 (2013) and prepares the way for a treatment of the gravitational case.