The canonical structure of Podolsky's generalized electrodynamics on the Null-Plane

TL;DR

This paper develops the canonical structure of Podolsky's generalized electrodynamics on the null-plane, analyzing constraints, gauge transformations, and boundary conditions unique to this formulation.

Contribution

It provides a detailed canonical analysis of Podolsky's theory on the null-plane, including constraint classification and gauge structure, which was not previously explored.

Findings

Identified second-class constraints unique to null-plane formulation

Established first-class constraints generating U(1) gauge transformations

Derived the generalized radiation gauge and discussed Dirac Brackets

Abstract

In this work we will develop the canonical structure of Podolsky's generalized electrodynamics on the null-plane. This theory has second-order derivatives in the Lagrangian function and requires a closer study for the definition of the momenta and canonical Hamiltonian of the system. On the null-plane the field equations also demand a different analysis of the initial-boundary value problem and proper conditions must be chosen on the null-planes. We will show that the constraint structure, based on Dirac formalism, presents a set of second-class constraints, which are exclusive of the analysis on the null-plane, and an expected set of first-class constraints that are generators of a U(1) group of gauge transformations. An inspection on the field equations will lead us to the generalized radiation gauge on the null-plane, and Dirac Brackets will be introduced considering the problem of uniqueness of these brackets under the chosen initial-boundary condition of the theory.