How can momentum be conserved during particle desintegration?

[boddhisattva]

Homework Statement

Given the desintegration of one particle,

1 -> 2 + 3

then show that

p1^2 = p2^2+p3² + 2cos(theta)*p2*p3

p1: momentum particle to be desintegrated
p2, p3: momentum of the two resulting particles
theta: angle between 2 & 3

Homework Equations

The Attempt at a Solution

I tried using conservation of quadrivector

 

[Polaris]

I am curious as to why you attempted this via 4-momentum? Is the text you are working with promote that use?

Anyways, the way I would approach this is a lot simpler, you do not need 4-momentum. Think of this by looking at the conservation of momentum thus,

P₁=P₂+P₃

and it follows that taking the inner product leads to

P₁$\cdot$P₁ = P₁² = (P₂+P₃)$\cdot$(P₂+P₃).

Leaving the rest to you. Essentially this is the laws of cosines.