# Four momentum squared and collisions

So, I am not asking is the square of four-momentum of a particle an invariant to Lorentz trasnformations, but rather,is it invariant in dynamic situations? It seems to me that this also has to hold. So, is four-momentum squared same before and after collision, not the total, but for one particle in that collision?

• four-momentum squared Is always c square – Eli Mar 3 '19 at 15:58
• Isnt it c squared times the mass squared with a minus in front? – Žarko Tomičić Mar 3 '19 at 15:59
• I don’t think so $P_{\mu }\cdot P^{\mu }=c^{2}$ – Eli Mar 3 '19 at 16:03
• The sign depends on your convention for writing 4-vectors or for forming scalar products. Obviously the convention used by particle physicists is superior in every way to that used by cosmologists. Obviously. – dmckee --- ex-moderator kitten Mar 3 '19 at 16:48
• I am not asking about the sign – Žarko Tomičić Mar 3 '19 at 16:55

As long as the particle has neither

• Changed kind (as happens in, for example, in charged-current weak scattering)
• Gotten excited (which can happen to atoms, nuclei, and hadrons; though in some cases this would be written as a change of type as in a proton turning into a Delta, for instance)

then the mass is the same.

But ... in a lot of ways what I wrote is a tautology. If a particle stays the same then it stays the same.

• So square of four momentum is constant for a particle given that its mass stays the same? – Žarko Tomičić Mar 3 '19 at 17:28
• The square of the four momentum is the mass (up to uninteresting constants). Of course the change or don't change together. – dmckee --- ex-moderator kitten Mar 3 '19 at 17:31
• I am just surprised i was solving compton scattering and somewher squared four momentum of an electron only to find out its equal to its mass!! I was puzzled.... – Žarko Tomičić Mar 3 '19 at 17:34
• Ah. Either your resource has done you a disservice my not making that connection clear or you didn't notice the importance at first. But either way you have it now. – dmckee --- ex-moderator kitten Mar 3 '19 at 17:39