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Meaning of this operator

  1. Oct 5, 2006 #1
    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 :blushing: )

    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]
  2. jcsd
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