Multipole Expansion in Generalized Electrodynamics

TL;DR

This paper develops a multipole expansion framework for Podolsky Electrodynamics in static regimes, enabling precise approximations of electromagnetic fields and proposing potential experimental tests for the theory.

Contribution

It introduces a systematic multipole expansion method for Podolsky Electrodynamics and addresses truncation for practical approximations, extending classical electrostatics techniques.

Findings

Derived multipole expansion formulas for static Podolsky fields

Provided methods for truncating the series for practical use

Suggested experimental scenarios to test Podolsky theory

Abstract

In this article we study some classical aspects of Podolsky Electrodynamics in the static regime. We develop the multipole expansion for the theory in both the electrostatic and the magnetostatic cases. We also address the problem of consistently truncating the infinite series associated with the several kinds of multipoles, yielding approximations for the static Podolskian electromagnetic field to any degree of precision required. Moreover, we apply the general theory of multipole expansion to some specific physical problems. In those problems we identify the first terms of the series with the monopole, dipole and quadrupole terms in the generalized theory. We also propose a situation in which Podolsky theory can be experimentally tested.