polarization vector

A massive spin 1 particle has three degrees of polarization for the obvious reason that in its rest frame its spin vector can point in three different directions. The three polarization vectors 𝜀_𝜇⁽ᵃ⁾ are simply the three unit vectors pointing along the x, y, and z axes, respectively (a = 1, 2, 3): 𝜀_𝜇⁽¹⁾=(0,1,0,0), 𝜀_𝜇⁽²⁾=(0,0,1,0), 𝜀_𝜇⁽³⁾=(0,0,0,1). In the rest frame k^𝜇=(m,0,0,0) and so

k^𝜇𝜀_𝜇⁽ᵃ⁾=0

Since this is a Lorentz invariant equation, it holds for a moving spin 1 particle as well.