English Dictionary

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

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 𝜀𝜇⁽ᵃ⁾ are simply the three unit vectors pointing along the x, y, and z axes, respectively (a = 1, 2, 3): 𝜀𝜇⁽¹⁾=(0,1,0,0), 𝜀𝜇⁽²⁾=(0,0,1,0), 𝜀𝜇⁽³⁾=(0,0,0,1). In the rest frame k𝜇=(m,0,0,0) and so k𝜇𝜀_𝜇⁽ᵃ⁾=0 Since this is a Lorentz invariant equation, it holds for a moving spin 1 particle as well.