Second Order Gauge Theory

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama’s program. A novel field strength $G=\partial F+fAF$arisesbesidestheoneofthefirstordertreatment,$F=\partial A-\partial A+fAA$. 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.