# Relativistic particle decay

1. Nov 16, 2015

### whatisreality

A particle with mass M a rest decays into two particles a and b.

I know that Ea + Eb = Mc2, from conservation of energy. But I'm pretty confused about signs in the conservation of momentum equation, and I've actually seen two versions!

pa + pb = 0, so

pa = - pb.

But I've also seen pa = pb! I know one is magnitudes and the other takes account of directions. Both are right, but which applies for the situation described above? As in, don't they conflict?

2. Nov 16, 2015

### Matterwave

Momenta include directions as well as magnitudes, so you need to specify directions. In that case, the correct equation is: $\vec{p}_a+\vec{p}_b=0$ assuming you are in the rest frame of the parent particle.

3. Nov 16, 2015

### DrGreg

Some authors use bold font to denote a vector $\textbf{p}$ and an italic font to denote the length of a vector $p$. Under this convention, $$\textbf{p}_a = -\textbf{p}_b$$implies$$p_a = p_b$$Similarly for authors who denote a vector with an overarrow: $\vec{p}$

And then there are some authors who use no special font for vectors who would say:
$$p_a = -p_b$$implies$$|p_a| = |p_b|$$

4. Nov 16, 2015

### whatisreality

Oh, they were using bold letters on the website. Thanks, that solves it!