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My question probably has a simple answer, but I've been scratching my

head over it a little too long so I thought I would ask it here. I

have three initial photons involved in a collision with 4-momenta k1,

k2 and k3. I have two reference frames:

frame 1: the centre of mass frame of photons k1 and k2 (so that 3-momenta k1+k2=0)

frame 2: the centre of mass frame of all photons k1, k2 and k3 (sothat 3-momenta k1+k2+k3=0)

I want to find out what the relativistic beta v/c and gamma 1/Sqrt(1-(v/c)^2 are. So there seems no way to directly find the relative velocity of the two frames is as only photons are involved. I thought

to use the expression for the relativistic doppler shift, but that doesn't seem appropriate.

Can anyone help me out here?

cheers.