Phase velocity and group velocity
= Phase velocity and group velocity
For a dispersion relation $\omega(k)$, the phase velocity is $c_p=\omega/k$ and the group velocity is $c_g=d\omega/dk$. For the Klein-Gordon relation at $k>0$,
$$
c_p=c\frac{\sqrt{k^2+A^2}}{k}>c,
\qquad
c_g=c\frac{k}{\sqrt{k^2+A^2}}<c,
\qquad
c_pc_g=c^2.
$$