Polarizationvectorn

Polarizationvectorn, often referred to as the polarization vector n or as a polarization reference vector, is a term used across physics to describe the orientation of a wave’s electric field or the helicity states of a massless gauge boson. In classical electromagnetism, a plane wave with wavevector k can be written with an electric field E(r,t) proportional to a polarization vector ε, which is perpendicular to k (k · ε = 0). The polarization vector encodes the state of polarization: a real ε describes linear polarization, while complex combinations represent circular or elliptical polarization. Normalization typically sets ε to unit length.

In quantum field theory and related computational formalisms, a similar construction appears with a reference light-like vector n^μ. Polarization vectors ε^μ_±(k, n) for a massless gauge boson depend on both the momentum k and the reference vector n. They satisfy k_μ ε^μ_± = 0 and ε^μ_+ ε_μ^− = -1. Changing the reference vector n^μ corresponds to a gauge transformation, leaving physical observables invariant. This use of n as a computational aid helps define helicity states and simplify amplitudes.

Beyond particle physics, polarization vectors also describe the direction of dipole oscillation in anisotropic media and are used in optics formalisms such as Jones calculus and Stokes parameters to represent and manipulate polarization states.

Overall, the polarization vector is a mathematical tool that captures the orientation and type of polarization of a field, with its exact interpretation depending on the physical context.