2
$\begingroup$

I am just reading about the Maurer-Cartan form in the context of Lie Groups, although the mathematical definition: $$\Theta(g)({\bf v}) = (L_{g^{-1}})_{*g}({\bf v})$$ for $g\in G$, $G$ a Lie group, ${\bf v}\in T_g(G)$, seems to be clear for me, I am trying to complement this with some physical intuition. Is there a nice simple application of this 1-form in basic physics, such as in mechanics?

Does it receive another name perhaps within physics in more advanced contexts? I am aware it is related to connections in fiber bundles and connections are related to gauge potentials, but this doesn't seem to provide me with any intuition on the Maurer-Cartan form on its own.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
3
$\begingroup$

Maurer-Cartan (MC) equations are e.g. used in:

References:

  1. J.E. Marsden and T.S. Ratiu, Intro to Mechanics and Symmetry, 2nd Eds, 1998.

  2. B. Kolev, Lie Groups and mechanics: an intro, arXiv:math-ph/0402052.

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thank you for the references, however I am wondering about the form itself, not necessarily the MC equations. I am trying to understand the form in a simple physical case if possible, the second reference just speaks about the isomorphism induced between $TG$ and $G\times\mathfrak{g}$ $\endgroup$
    – ohneVal
    Commented Aug 20, 2019 at 14:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.