polarization vector

English

Noun

polarization vector (plural polarization vectors)

1. (quantum field theory) One of a set of three spacelike (and possibly also one timelike) four-dimensional vectors which are orthonormal within some inertial reference frame.
   • 2003, A. Zee, Quantum field theory in a nutshell, Princeton, New Jersey: Princeton University Press, §I.5, page 32:

     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 ${\displaystyle \epsilon _{\mu }^{(a)}}$ are simply the three unit vectors pointing along the x, y, and z axes, respectively (a = 1, 2, 3): ${\displaystyle \epsilon _{\mu }^{(1)}=(0,1,0,0)}$, ${\displaystyle \epsilon _{\mu }^{(2)}=(0,0,1,0)}$, ${\displaystyle \epsilon _{\mu }^{(3)}=(0,0,0,1)}$. In the rest frame ${\displaystyle k^{\mu }=(m,0,0,0)}$ and so
             ${\displaystyle k^{\mu }\epsilon _{\mu }^{(a)}=0}$
     Since this is a Lorentz invariant equation, it holds for a moving spin 1 particle as well.