a characteristic of the state of a particle; it is associated with the particle’s possession of an intrinsic angular momentum, or spin. The concept of particle polarization is close to that of the polarization of light. The latter concept means in particular that plane light waves of a given frequency, direction of propagation, and intensity may differ in polarization—that is, in the arrangement of the vectors of the electric and magnetic field strengths in space. This property is preserved in the quantum description of light; thus, a photon may have polarization.
A particle with nonzero rest mass—such as an electron or nucleus—and spin J, in units of Planck’s constant ℏ, has 2J + 1 quantum states that correspond to different orientations of the spin—that is, to different values of the projection of the spin in a given direction. The state of the particle is a superposition of these states. If the superposition coefficients are completely defined (a pure quantum state), then the particle is said to be completely polarized. If the superposition coefficients are not completely defined but are specified only by some statistical characteristics (a mixed state), we speak of partial polarization. A particle may be completely unpolarized; this means that its properties are identical in all directions, as is the case with a spinless particle, for which J = 0. In the general case, the polarization of a particle determines the degree of symmetry, or asymmetry, of the particle in space. A particle is said to be polarized in the narrow sense of the word if its symmetry characteristics include an axis such as a rotating solid body or a circularly polarized light has. If both a screw axis and spherical symmetry are absent, the polarization is referred to as alignment; an example is linearly polarized light. The polarization of particles is in general determined by the number of parameters, which is equal to (2J + 1)2 — 1.
A particle with zero mass, such as a photon, has only two states, which are determined by its spin; in the general case, its polarization is determined by three parameters. Neutrinos with zero mass have the special property of always possessing complete right-handed or left-handed circular polarization.
V. B. BERESTETSKII