= Four-wavevector
{title2=$K^\mu=(\omega/c,\mathbf k)$}
= Wave four-vector
{synonym}
The <four-wavevector> combines the <angular frequency> and spatial <wavevector> of a plane wave. Phase invariance gives $K'^\mu=\Lambda^\mu{}_{\nu}K^\nu$. Under a boost $\mathbf v$, $\omega'=\gamma(\omega-\mathbf v\cdot\mathbf k)$, $\mathbf k'_\parallel=\gamma(\mathbf k_\parallel-\omega\mathbf v/c^2)$ and $\mathbf k'_\perp=\mathbf k_\perp$. For metric signature $(+,-,-,-)$, $R_\mu K^\mu=\omega t-\mathbf k\cdot\mathbf r$ is a <Lorentz scalar>. A vacuum light wave has $K_\mu K^\mu=0$.
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