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.
Highlights
Quantum electrodynamics (QED) renormalization program.Historically, the problem of infinities first arose in the classical electrodynamics of point particles in the 19th and early20th century
We demonstrate that the BP model solution for a point charge in electrodynamics corresponds to an ordinary electrodynamic solution for a specific charge distribution
We demonstrated that the BP model solution for a point charge in classical electrodynamics corresponds to an ordinary classical electrodynamic solution for a specific charge distribution given by Eq (23)
Summary
In the case of the Lorenz gauge, a natural gauge-fixing term originally introduced by Podolsky and Kikuchi [12] which considerably simplifies the calculation in the quantization process has long been passed without notice in the literature and has been only recently rescued by Bufalo, Pimentel and Soto [27]. The role of this term in obtaining a simple generalized photon propagator in a straightforward manner cannot be overemphasized. For a point charge delta distribution, the BP model leads to a everywhere finite potential – we shall show that it is possible to generate this very same potential within the scope of ordinary electrodynamics using a suitable charge distribution
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