Proca action
In physics, specifically field theory and particle physics, the Proca action describes a massive spin-1 field of mass m in Minkowski spacetime. The corresponding equation is a relativistic wave equation called the Proca equation. The Proca action and equation are named after Romanian physicist Alexandru Proca.
The Proca equation is involved in the Standard model and describes there the three massive vector bosons, i.e. the Z and W bosons.
This article uses the (+−−−) metric signature and tensor index notation in the language of 4-vectors.
Lagrangian density
The field involved is a complex 4-potential Bμ = (φ/c, A), where φ is some kind of a generalized electric potential and A is a generalized magnetic potential. The field 
transforms like a complex four-vector.
The Lagrangian density is given by:
where c is the speed of light, ħ is the reduced Planck constant, and ∂μ is the 4-gradient.
Equation
The Euler–Lagrange equation of motion for this case, also called the Proca equation, is:
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