Vile spinors in odd dimensions?

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SUMMARY

The discussion centers on the impossibility of having Weyl spinors in odd dimensions. It is established that the existence of Weyl spinors requires both right-handed and left-handed components, which cannot coexist in odd-dimensional spaces. This limitation arises from the mathematical properties of spinors and their transformation under Lorentz groups in such dimensions.

PREREQUISITES
  • Understanding of Weyl spinors and their properties
  • Familiarity with Lorentz transformations
  • Knowledge of dimensionality in physics
  • Basic concepts of spinor representation theory
NEXT STEPS
  • Research the mathematical framework of spinor representation theory
  • Explore the implications of dimensionality on particle physics
  • Study the properties of Lorentz groups in various dimensions
  • Investigate the role of chirality in quantum field theory
USEFUL FOR

The discussion is beneficial for theoretical physicists, mathematicians specializing in representation theory, and students studying quantum field theory and its implications in different dimensional spaces.

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Why is it not possible to have Weyl spinors in odd dimensions?
 
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Because there has to be a right-handed one and a left-handed one?
 

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