
#1
Oct506, 02:22 AM

P: 134

From the "Lie Group" theory point of view we know that:
[tex] p [/tex] := is the generator for traslation (if the Lagrangian is invariant under traslation then p is conserved) [tex] L [/tex]:= 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: [tex] pf(x)\rightarrow \frac{df}{dx} [/tex] 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 [tex] \psi [/tex] 


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