Duality considerations about the Maxwell-Podolsky theory through the symplectic embedding formalism and spectrum analysis

TL;DR

This paper derives a gauge-invariant dual version of the Maxwell theory with a mass term using symplectic embedding, revealing a higher-order derivative structure and analyzing the spectrum for stability and unitarity.

Contribution

It introduces a novel dual formulation of the Maxwell-Podolsky theory via symplectic embedding, preserving gauge symmetry and analyzing its spectral properties.

Findings

The dual theory includes a higher-order derivative term.

The gauge invariance of the dual theory is preserved.

Spectrum analysis reveals conditions for unitarity and stability.

Abstract

We find the dual equivalent (gauge invariant) version of the Maxwell theory in D=4 with a Proca-like mass term by using the symplectic embedding method. The dual theory obtained (Maxwell-Podolsky) includes a higher-order derivative term and preserve the gauge symmetry. We also furnish an investigation of the pole structure of the vector propagator by the residue matrix which considers the eventual existence of the negative-norm of the theory.