Obtaining an expression for the Lorentz Force in the Dirac theory

Question

We know that $P = p - \frac{e}{c} A$

How can we obtain a expression for the Lorentz force from the equation above using the Dirac Theory??

Could you please explain this to me step by step?

The only idea I have now is: $i\hbar \frac{dP}{dt} = [P,H]$

Answer 1

Hint: you may write the Dirac equation

$$(i \hbar \gamma^\mu \partial_\mu - mc) \psi = 0 $$

with the minimal coupling ansatz

$$\partial_{\mu} \rightarrow \partial_{\mu}+ieA_{\mu}$$

And you may find the following reference useful