By reflection of photons from a mirror, the mirror must get an impulse of 2p=h/pi.l for every photon. This means that the mirror receives kinetic energy. But the photon has the energy it has before the refection. How does QED explain this? In "Photons and perfect mirror" the question is answered as a consequence of other explanation but I does not see the mechanism which leads to it. I try to clarify this as respond to the answers.
QED uses Feynman diagrams and they are written in the center of mass. In the case of a photon hitting a mirror, it is hitting the field of electrons in the outer band of the mirroring substance. For reflection there should be elastic scattering in the center of mass so that the phases of the photons are kept and the image emerges intact on reflection. So it should be a QED feynman diagram of a photon scattering elastically off a field.
The kinematics are similar to a ball bouncing off a wall, i.e. elastically scattering. The assumption is that the mass of the wall is practically infinite and the center of mass with respect to the ball+wall, where the elastic scattering happens is at the same (x,y,z) as the center of mass of the wall itself.
For the photon and the collective electric field of the electrons it is scattering off, the center of mass and the laboratory frame are practically the same, as the photon has zero mass and low energy (optical photons). Even the mass of a single electron , (.5MeV, gamma ray energies are of this size) is large enough for the lab frame to be considered the same as the center of mass frame. The effect of the transformation to the lab on the energy of the photon will be very very small.