Hermitian Conjugate of Spinors: Is it Equal?

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SUMMARY

The hermitian conjugate of the expression \(\epsilon \sigma^\mu \psi^\dagger\) is definitively equal to \(-\psi \sigma^\mu \epsilon^\dagger\), where both \(\psi\) and \(\epsilon\) are 2-component spinors with Grassmann parity 1. This conclusion is established based on the properties of hermitian conjugates and the behavior of spinors under conjugation. The discussion clarifies the correct terminology regarding Grassmann numbers and emphasizes the importance of understanding spinor algebra in this context.

PREREQUISITES
  • Understanding of spinor algebra
  • Familiarity with Grassmann numbers
  • Knowledge of hermitian conjugates in quantum mechanics
  • Basic concepts of quantum field theory
NEXT STEPS
  • Study the properties of Grassmann numbers in detail
  • Learn about hermitian conjugation in quantum mechanics
  • Explore spinor representations in quantum field theory
  • Investigate the implications of Grassmann parity in physical theories
USEFUL FOR

The discussion is beneficial for theoretical physicists, quantum field theorists, and students studying advanced quantum mechanics, particularly those focusing on spinor fields and their mathematical properties.

alphaone
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I just have a simple question about hermition conjugates of spinors. Is the hermitian conjugate of:
\epsilon \sigma^\mu \psi^\dagger
equal to:
-\psi \sigma^\mu \epsilon^\dagger
where both psi and epsilon are 2-component spinors of grassmann numbers?
 
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"spinors of Grassmann parity 1" you should have written.

As to the question, the answer is "yes".
 

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