Four-frequency

The four-frequency of a photon is defined by

:$N^a\; =\; left(\; u,\; u\; mathbf\{n\}\; ight)$

where $u$ 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

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

where $omega=2\; pi\; u$, $c$ 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 $c=\; u\; lambda$) by

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