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Spinors and Lorentzgroups: representation of the complete Lorentzgroup?

  1. Dec 25, 2011 #1
    1. The problem statement, all variables and given/known data


    This question is about Lorentzgroups. In my course of Relativity, we've seen a very little about representations of complete Lorentz groups but there are two little exercises, which we can do, but I do not understand what should be checked, not even how to start this.

    The question is the following:
    A/Does the Lagrangian L = i u*^{Adot} \partial_{A Adot} u^{Adot} (with u^A a spinor field and u* a conjugated spinor) form a scalar under the complete Lorentzgroup?

    B/What about the Lagrangian L = F_{mu nu} F*^{mu nu}, and I suppose this F is the Electromagnetic Maxwell Tensor (http://en.wikipedia.org/wiki/Electromagnetic_tensor)

    2. Relevant equations


    3. The attempt at a solution

    Don't even understand the meaning of "a scalar under the complete Lorentzgroup".

    Thanks for any help you can offer and a Merry Christmas to all of you!

  2. jcsd
  3. Dec 27, 2011 #2


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    Science Advisor
    Homework Helper

    What is a scalar in general and <under the restricted Lorentz group> ? Look this notion up in your notes.
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