Spinor Representations: Intuitive Understanding

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SUMMARY

The discussion centers on the transformation properties of Majorana spinors in the context of special orthogonal groups SO(D-1) and SO(D-2). It establishes that massive Majorana spinors exhibit D-1 degrees of freedom, while massless Majorana spinors correspond to D-2 degrees of freedom. This parallels the behavior of vector bosons, reinforcing the understanding of spin states in quantum field theory. The inquiry emphasizes the need for clarity in the transformation of spin states within these mathematical frameworks.

PREREQUISITES
  • Understanding of Majorana spinors
  • Familiarity with special orthogonal groups (SO(D-1) and SO(D-2))
  • Knowledge of degrees of freedom in quantum field theory
  • Basic concepts of massive and massless particles
NEXT STEPS
  • Study the properties of Majorana spinors in quantum field theory
  • Explore the mathematical structure of special orthogonal groups SO(D-1) and SO(D-2)
  • Investigate the degrees of freedom associated with different particle types
  • Learn about the implications of spin state transformations in particle physics
USEFUL FOR

Physicists, particularly those specializing in quantum field theory, theoretical physicists, and students seeking a deeper understanding of spinor representations and their transformations.

gentsagree
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Can you give me an intuitive understanding of the following:

"The spin states of massive and massless Majorana spinors transform in representations of SO(D-1) and SO(D-2), respectively".

I see the similarity with vectors bosons, where massive vectors have d-1 degrees of freedom and massless have d-2, but what exactly is meant by "the spin states of (...) Majorana spinors transform"?
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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