Question

Lorentz transformations
a) A photon with energy Eph in a reference frame S moves at an angle θ with respect
to the y axis, in the x-y plane (i.e., its propagation vector is

ˆk = (sin θ, cos θ, 0)).

Write out the photon’s momentum four-vector p
μ
ph in frame S.

Answer 1

Photon's four-momentum vector is given by :

$p^\mu = \begin{pmatrix} \frac{E_{ph}}{c}\\ \frac{E_{ph}}{c} \;sin\;\theta\\ \frac{E_{ph}}{c}\;cos\;\theta\\ 0\\ \end{pmatrix}$