Green functions and propagation in the Bopp–Podolsky electrodynamics

Abstract

In this paper, we investigate the so-called Bopp–Podolsky electrodynamics. The Bopp–Podolsky electrodynamics is a prototypical gradient field theory with weak nonlocality in space and time. The Bopp–Podolsky electrodynamics is a Lorentz and gauge invariant generalization of the Maxwell electrodynamics. We derive the retarded Green functions, first derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, generalized Liénard–Wiechert potentials and the corresponding electromagnetic field strengths in the framework of the Bopp–Podolsky electrodynamics for three, two and one spatial dimensions. We investigate the behaviour of these electromagnetic fields in the neighbourhood of the light cone. In the Bopp–Podolsky electrodynamics, the retarded Green functions and their first derivatives show fast decreasing oscillations inside the forward light cone.