Understanding Particle Decay and Momentum Conservation in Relativity

[planesinspace]

I am answering a question about a particle decaying into two other particles and one needs to find the momentum of the children particles from the rest frame of the parent. I found a very helpful article on Wikipedia under 'Particle Decay', however I am really confused by their mathematical working and wondering if anyone can explain it or agree with me that Wiki has made a mistake :)

I can't copy all the equations so the link is here: http://en.wikipedia.org/wiki/Particle_decay
its under the Sub heading Conservation of four momentum.

I don't understand how they can expand 2(p_M*p_1) into only 2 terms when under normal (a+b)(c+d) expansions you get four. Unless there is some weird vector multiplication I don't understand?

Any help GREATLY appreciated!

 

[tom.stoer]

That easy. Each momentum p in these equations is a four-momentum, so for p this reads p = (E, p). The multiplication is just the vector multiplication, where the first term involves the E's, whereas the second term involves the three-momentum p. The minus sign appears due to the law how to multiply co- and contra-variant four-vectors.

 

[planesinspace]

Thankyou!