Four-frequency

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The four-frequency of a photon is defined by

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

where $ν$ 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 $ω = 2πν$ , $c$ is the speed of light and $\mathbf{k}=\frac{2 \pi}{\lambda}\mathbf{n}$ and $λ$ 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 $c = νλ$ ) by