Second Order Gauge Theory

TL;DR

This paper develops a second order gauge theory with a new field strength, deriving conserved currents and topological terms, and applies it to Podolsky electrodynamics and SU(N) infrared analysis.

Contribution

It introduces a novel second order gauge theory framework with a new field strength and topological terms, extending previous gauge theories.

Findings

Derived a new second order gauge field strength G.

Obtained conserved currents and topological terms from local invariance.

Applied the theory to Podolsky electrodynamics and analyzed SU(N) infrared behavior.

Abstract

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength $G=\partial F+fAF$ arises besides the one of the first order treatment, $F=\partial A-\partial A+fAA$. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is $L_{P}\propto G^{2}$. In this application the photon mass is estimated. The SU(N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian.