Light-front gauge invariant formulation and electromagnetic duality

TL;DR

This paper develops a gauge invariant light-front formulation of Maxwell's equations, introduces a novel canonical quantization method based on the kinematic generator, and explores electromagnetic duality and photon propagators within this framework.

Contribution

It presents a new light-front gauge invariant formulation, a novel canonical quantization approach, and an equivalent Lagrangian density involving two gauge potentials.

Findings

Covariant photon propagators consistent with Schwinger's source theory.

Canonical quantization based on $P^{+}$ for electromagnetic fields.

Light-front formulation accommodating electric and magnetic external currents.

Abstract

The gauge invariant formulation of Maxwell's equations and the electromagnetic duality transformations are given in the light-front (LF) variables. The novel formulation of the LF canonical quantization, which is based on the kinematic translation generator $P^{+}$ rather then on the Hamiltonian $P^{-}$, is proposed. This canonical quantization is applied for the free electromagnetic fields and for the fields generated by electric and magnetic external currents. The covariant form of photon propagators, which agrees with Schwinger's source theory, is achieved when the direct interaction of external currents is properly chosen. Applying the path integral formalism, the equivalent LF Lagrangian density, which depends on two Abelian gauge potentials, is proposed. Some remarks on the Dirac strings and LF non local structures are presented in the Appendix.