In field theory, the Proca action describes a massive spin-1 field of mass m in Minkowski spacetime. The field involved is a real vector field A. The Lagrangian density is given by:

<math>\mathcal{L}=-\frac{1}{4}(\partial^\mu A^\nu-\partial^\nu A^\mu)(\partial_\mu A_\nu-\partial_\nu A_\mu)+\frac{m^2}{2}A^\mu A_\mu<math>

(+---) signature

The Euler-Lagrange equation is

<math>\partial_\mu(\partial^\mu A^\nu - \partial^\nu A^\mu)+m^2 A^\nu=0<math>

which is equivalent to

<math>(\partial_\mu \partial^\mu+m^2)A_\nu=0<math>

and

<math>\partial_\mu A^\mu=0<math>

The Proca action is the gauge-fixed version of the Stückelberg action via the Higgs mechanism.