# Noether's theorem

Can anyone explain to me where the functions $$F$$ and $$Q$$ come from?

For what it is worth, both $$Q^{\alpha}$$ and $$F$$ are objects that need to exist before we can apply Noether's theorem, i.e. they are assumptions. $$Q^{\alpha}$$ is the assumed infinitesimal transformation of the variable $$q^{\alpha}$$, while the total time-derivative of $$F$$ is assumed to be the infinitesimal change of the Lagrangian under said infinitesimal transformation, cf. eq. (7.2).