Four-frequency

$N^a\; =\; left(nu,\; nu\; mathbf\{n\}\; right)$

where $nu$ is the photon's frequency and $mathbf\{n\}$ is a unit vector in the direction of the photon's motion. The four-frequency is always a null vector. Closely related to the four-frequency is the wave four-vector defined by

$K^a=left(frac\{omega\}\{c\},\; mathbf\{k\}right)$

where $omega=2\; pi\; nu$, $c$ is the speed of light and $mathbf\{k\}=frac\{2\; pi\}\{lambda\}mathbf\{n\}$ and $lambda$ is the wavelength of the photon. The wave four-vector is more often used in practice than the four-frequency, but the two vectors are related (using $c=nu\; lambda$) by

$K^a=frac\{2\; pi\}\{c\}N^a$