Spinors and Lorentzgroups: representation of the complete Lorentzgroup?

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SUMMARY

The discussion focuses on the representation of the complete Lorentz group in the context of two Lagrangians: L = i u*^{Adot} ∂_{A Adot} u^{Adot} and L = F_{mu nu} F*^{mu nu}. The first Lagrangian involves a spinor field, while the second relates to the Electromagnetic Maxwell Tensor. The primary question is whether these Lagrangians form scalars under the complete Lorentz group, a concept that requires understanding the definition of scalars in this context.

PREREQUISITES
  • Understanding of Lorentz groups and their representations
  • Familiarity with spinor fields and their properties
  • Knowledge of Lagrangian mechanics in the context of field theory
  • Basic comprehension of the Electromagnetic Maxwell Tensor
NEXT STEPS
  • Study the properties of scalars under the complete Lorentz group
  • Explore the mathematical formulation of spinor fields in quantum field theory
  • Investigate the role of the Electromagnetic Maxwell Tensor in relativistic physics
  • Review Lagrangian mechanics and its application to field theories
USEFUL FOR

Students of theoretical physics, particularly those studying relativity and quantum field theory, as well as researchers interested in the mathematical foundations of particle physics.

Trinitiet
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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



/

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

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