Reduced-order Bopp-Podolsky model on the null-plane

TL;DR

This work presents a null-plane (light-front) canonical analysis of the reduced-order Bopp-Podolsky electrodynamics, implemented by introducing an auxiliary vector field $B_\mu$ that decouples into a massive Podolsky sector and a massless Maxwell sector for $A_\mu$. By formulating the theory on null-plane coordinates with evolution parameter $x^+$, the authors derive the full Dirac-Bergmann constraint structure, identify two first-class gauge generators, and separate two independent second-class constraint sectors. They construct the Dirac matrix, compute the Dirac brackets, and show that the second-class constraints can be imposed strongly, yielding an Abelian first-class theory that preserves gauge invariance. The resulting framework reveals nonlocalities inherent to null-plane dynamics and confirms the mass-generation mechanism within a gauge-invariant, reduced-order BP model, with implications for quantization and further physical applications.

Abstract

We consider the null-plane dynamics for a reduced-order version of the higher-derivatives Bopp-Podoslky generalized electrodynamics model. By introducing an auxiliary vector field, we achieve a simpler equivalent version with lower derivatives. The massive and massless modes for the Podolsky gauge field get split into two sectors. We describe the model in terms of light-front coordinates and, by choosing $x^+$ as a natural evolution parameter, proceed to its null-plane dynamics analysis obtaining the whole constraints structure and canonical field equations. After a convenient constraints redefinition, we calculate the Dirac brackets corresponding to the second-class sector. Gauge invariance is preserved and, after elimination of second-class constraints, we obtain a consistent Abelian first-class theory for the reduced-order Bopp-Podolsky model.