In physics, in the area of 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:
The above presumes the metric signature (+---). Here, c is the speed of light and is Dirac's constant. In the dimensionless units commonly employed in theoretical physics, these may both be taken to be one. The Euler-Lagrange equation of motion is (this is also called the Proca equation):
which is equivalent to the conjunction of
Quantizing the Proca action requires the use of second class constraints.