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

TL;DR

This paper analyzes a simplified version of the higher-derivative Bopp-Podolsky electrodynamics model on the null-plane, revealing its constraint structure, gauge invariance, and canonical dynamics using light-front coordinates.

Contribution

It introduces a reduced-order Bopp-Podolsky model with an auxiliary field, providing a detailed null-plane Hamiltonian analysis and preserving gauge invariance.

Findings

Separated massive and massless modes into two sectors.

Derived the complete constraint structure and Dirac brackets.

Established a consistent first-class gauge theory for the reduced model.

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.