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Homework Help: Manifolds and Lorentz-group

  1. Jan 10, 2009 #1
    1. The problem statement, all variables and given/known data
    I've got a problem. I should discribe all minimal invariant manifolds in Minkowski-space, where the proper Lorentz-group [tex] \mathcal{L}_{+}^{\uparrow} [/tex] acts transitivly (i.e. any two points of the manifold can be transformed into each other by a Lorentz-transformation).

    2. Relevant equations

    3. The attempt at a solution
    My problem is that I don't really understand what I should do. For example: what is meant by a minimal invariant manifold? What has a manifold to do with a group at all?

    The only thing that I know for sure is: [tex] \Lambda \in \mathcal{L}_{+}^{\uparrow} \Rightarrow \mathrm{det} \Lambda = 1 [/tex] and [tex] \Lambda^{0}_{0} \geq 1 [/tex] and [tex] \mathcal{L}_{+}^{\uparrow} [/tex] contains rotations and Lorentz-boosts.

    I'm really looking forward to get some help for this exercise.
     
  2. jcsd
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