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 Lienard-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.

23 pages

References in corpus (3)

• Path Integral Quantization of Generalized Quantum Electrodynamics
• On gradient field theories: gradient magnetostatics and gradient elasticity
• Renormalizability of generalized quantum electrodynamics

Cited by in corpus (3)

• Second gradient electromagnetostatics: electric point charge, electrostatic and magnetostatic dipoles
• Second gradient electrodynamics: a non-singular relativistic field theory
• Second gradient electrodynamics: Green functions, wave propagation, regularization and self-force