From the "Lie Group" theory point of view we know that:(adsbygoogle = window.adsbygoogle || []).push({});

[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]

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Meaning of this operator

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Meaning operator | Date |
---|---|

A The meaning of the commutator for two operators | Jan 9, 2018 |

I Meaning of mapping R[X]->Maps[R,R] | Apr 15, 2017 |

I What does this symbol mean?? | Oct 27, 2016 |

I Matrix Rings - Basic Problem with Meaning of Notation | Oct 8, 2016 |

Does n*a ALWAYS mean to a + a + + a (n times) where + is the group operation? | Oct 15, 2012 |

**Physics Forums - The Fusion of Science and Community**