# Meaning of this operator

1. Oct 5, 2006

From the "Lie Group" theory point of view we know that:

$$p$$ := is the generator for traslation (if the Lagrangian is invariant under traslation then p is conserved)

$$L$$:= s the generator for rotation (if the Lagrangian is invariant under traslation then L is conserved)

(I'm referring to momentum p and Angular momentum L, although the notation is obvious )

My question is if we take the "Lie derivative" and "covariant derivative" as a generalization of derivative for curved spaces.. if we suppose they're Lie operators..what's their meaning?..if the momentum operator acts like this:

$$pf(x)\rightarrow \frac{df}{dx}$$ derivative of the function..could the same holds for Lie and covariant derivative (covariant derivative is just a generalization to gradient, and i think that Lie derivatives can be expressed in some cases as Covariant derivatives, in QM the momentum vector applied over the wave function is just the gradient of the $$\psi$$