# Relativistic particle decay

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?

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Matterwave
Gold Member
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.

DrGreg
Gold Member
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$$|p_a| = |p_b|$$

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$$|p_a| = |p_b|$$
Oh, they were using bold letters on the website. Thanks, that solves it!