Do the Energy-Momentum Transformations apply to Photons?

[Dale]

In these strict sense rest frame could be applicable for a few kind of single elementary particles

Which is precisely why the term "center of momentum frame" is so common in the particle physics literature.

This convention is not universally used, but it is more descriptive and is appealing to many scientists.

 

[vanhees71]

Indeed the term "center of momentum frame" is the most precise expression for "rest frame", if not the only correct one at all, of a composite system.

 

[PeterDonis]

The theory of relativity excludes rigid bodies.

More precisely, it excludes bodies in which internal forces are propagated faster than light. But it is perfectly possible to have rigid motions of bodies, under appropriate conditions.