Generalization of the Proca Action

Understand

We consider the Lagrangian of a vector field with derivative self-interactions with a priori arbitrary coefficients.

• Starting with a flat space-time we show that for a special choice of the coefficients of the self-interactions the ghost-like pathologies disappear.
• For this we use the degeneracy condition of the Hessian.
• This constitutes the Galileon-type generalization of the Proca action with only three propagating physical degrees of freedom.