Proca action
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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 Planck'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
which is equivalent to the conjunction of
with
which is the Lorenz gauge condition.
The Proca action is the gauge-fixed version of the Stückelberg action via the Higgs mechanism.
Quantizing the Proca action requires the use of second class constraints.
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