# Pauli-Villars Regularization Elucidated in Bopp-Podolsky's Generalized Electrodynamics

## TL;DR

This paper elucidates how Bopp-Podolsky's generalized electrodynamics inherently incorporates Pauli-Villars regularization through its photon propagator, linking the regularization scale to a fundamental length parameter and exploring its physical implications.

## Contribution

It demonstrates a gauge-independent Pauli-Villars regularization mechanism within Bopp-Podolsky's electrodynamics and clarifies the physical meaning of its length parameter in relation to charge distribution size.

## Key findings

- Photon propagator includes built-in Pauli-Villars regularization
- Parameter 'a' inversely related to regularization mass scale
- Explicit solutions relate 'a' to charge distribution size

## Abstract

We discuss an inherent Pauli-Villars regularization in Bopp-Podolsky's generalized electrodynamics. Introducing gauge-fixing terms for Bopp-Podolsky's generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli-Villars regularization independent of the gauge choice made in Maxwell's usual electromagnetism. According to our realization, the length dimensional parameter $a$ associated with Bopp-Podolsky's higher order derivatives corresponds to the inverse of the Pauli-Villars regularization mass scale $\Lambda$, i.e. $a = 1/\Lambda$. Solving explicitly the classical static Bopp-Podolsky's equations of motion for a specific charge distribution, we explore the physical meaning of the parameter $a$ in terms of the size of the charge distribution. As an offspring of the generalized photon propagator analysis, we also discuss our findings regarding on the issue of the two-term vs. three-term photon propagator in light-front dynamics.