1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basic question about Z2 graded algebras

  1. Nov 17, 2007 #1
    Sorry, I really hate reading, and I do better by just asking stupid questions.

    The lorentz group SO(3,1) is not simply connected so its unitary representation is in a projective space. It's fundamental group is [tex]\mathbb{Z}_2[/tex]
    so picking your standard path a certain way you can get

    [tex]U(\bar \Lambda )U(\Lambda ) = \pm U(\bar \Lambda \Lambda )[/tex]

    Now if you use the universal cover of SO(3,1), [tex]SL(2,\mathbb{C})[/tex] you can get

    [tex]U(\bar \Lambda )U(\Lambda ) = U(\bar \Lambda \Lambda )[/tex]

    Now my question is by introducing the gradation are you basically just redefining your unitary transformations so that [tex]U(\bar \Lambda )U(\Lambda ) = U(\bar \Lambda \Lambda )[/tex] for SO(3,1) too?
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Basic question about Z2 graded algebras