Prove Lorentz invariance for momentum 4-vector

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1. May 5, 2016

flintbox

1. The problem statement, all variables and given/known data
I am meant to show that the following equation is manifestly Lorentz invariant:
$$\frac{dp^{\mu}}{d\tau}=\frac{q}{mc}F^{\mu\nu}p_{\nu}$$

2. Relevant equations
I am given that $F^{\mu\nu}$ is a tensor of rank two.

3. The attempt at a solution
I was thinking about doing a Lorents transformation to this four vector, but I don't know what this would yield.

2. May 5, 2016

Fightfish

Well then why not try it? When we say that an equation is Lorentz invariant, what we mean is that it holds true in all (inertial) reference frames accessible via a Lorentz transformation. So, that means that you have to show that if
$$\frac{dp^{\mu}}{d\tau}=\frac{q}{mc}F^{\mu\nu}p_{\nu}$$
then
$$\frac{dp^{\mu'}}{d\tau}=\frac{q}{mc}F^{\mu'\nu'}p_{\nu'}$$
is also true.

3. May 11, 2016

flintbox

You're right! Thank you so much.