Spinors and Lorentzgroups: representation of the complete Lorentzgroup?

[Trinitiet]

Homework Statement

Hi,

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)

Homework Equations

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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!

Trinitiet

 

[dextercioby]

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