Hi, I have just recently begun delving into SR, and there are a few questions I would like clarified if possible, with your assistance. NB These questions were discussed during some of the lectures and are NOT HW assignments. 1) If a particle of rest mass m breaks down, whilst at rest, into a particle of mass m' and a photon, what would be the energies of the particle with mass m' and the photon created in the process?: I understand that the four-momentum of the original particle of mass m is (m,0) and those of m' and the photon are (E,p) and (ε,εn^). I also understand that since the center of mass reference frame of the original particle is also that of the products (m' and the photon), the overall four-momentum must be conserved and the following equality must hold: Ptot = (m,0)=(E+ε,p+n^). What is not clear to me is why would that entail E + p = m? I don't quite understand this equality. What does it designate? What is its meaning? 2) In reference frame O two photons with frequencies [itex]\nu[/itex]1 and[itex]\nu[/itex]2 are moving in the positive and negative x^ directions, respectively. What would be the CM of the two photon's velocity wrt O? The four-momentum of the first photon may be written thus: h[itex]\nu[/itex]1(1,n^) Similarly for the second: h[itex]\nu[/itex]2(1,-n^). Now, the total four-momentum must be conserved: P = h([itex]\nu[/itex]1 + [itex]\nu[/itex]2, ([itex]\nu[/itex]1 - [itex]\nu[/itex]2)n^). What I don't quite understand is how applying Boost in the n^ direction at a velocity u would yield: h[itex]\gamma[/itex]([itex]\nu[/itex]1 - [itex]\nu[/itex]2-u([itex]\nu[/itex]1 + [itex]\nu[/itex]2)). Could someone please explain this delicate point to me step-by-step? 3) Suppose Pμ = (M + h[itex]\nu[/itex],h[itex]\nu[/itex]n^). Why does that squared yield: M2 + 0 + 2h[itex]\nu[/itex]M? What does the zero denote? Also, what is the difference between the following notations: Pμ and Pμ? I'd truly appreciate any insightful remarks.