Relativistic Particle Decay: Momentum Conservation

[whatisreality]

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

I know that E_a + E_b = 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!

p_a + p_b = 0, so

p_a = - p_b.

But I've also seen p_a = p_b! 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?

 

[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.

 

[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$$
|p_a| = |p_b|
$$

 

[whatisreality]

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!