How to show the covariant projection method?

Question

Hello,

I see that one popular method for forming bound states in Quantum Field Theory is the Covariant Projection Method  where we project onto desired Spin-1 states by replacing the $\upsilon$ $v$  spinor product with the Dirac matrix:

$$1)\ \frac{1}{\sqrt{2}}\not{\epsilon}\dfrac{\not{P}+M}{2}$$

Could you please help show it ? For example equation 2.1a here :

$$\upsilon(\uparrow)\bar{u}(\uparrow)=\frac{1}{\sqrt{2}}\not{\epsilon}(\uparrow)\dfrac{\not{P}+M}{2}$$

$\epsilon^\mu$ is the polarization vector of the meson and P , M are the 4-momentum and mass of the meson.

Thank you very much.