**Equation**

The Euler-Lagrange equation of motion for this case, also called the **Proca equation**, is:

which is equivalent to the conjunction of

with

which is the Lorenz gauge condition. When *m* = 0, the equations reduce to Maxwell's equations without charge or current. The Proca equation is closely related to the Klein-Gordon equation, because it is second order in space and time.

In the more familiar vector calculus notation, the equations are:

and is the D'Alembert operator.

Read more about this topic: Proca Action

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