Transformation matrix from Dirac to Weyl

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SUMMARY

The discussion focuses on constructing a transformation matrix S that converts Dirac representations of gamma matrices into Chiral representations. The matrix S must be both Hermitian and unitary. The user has derived an equation involving known matrices on both sides of the equation, indicating a need for a systematic approach to isolate and solve for S. A suggested starting point is to express ##\gamma_D^5## in the last equation to facilitate the solution process.

PREREQUISITES
  • Understanding of Dirac and Chiral representations of gamma matrices
  • Knowledge of Hermitian and unitary matrices
  • Familiarity with matrix equations and manipulation
  • Basic concepts of quantum mechanics and spinors
NEXT STEPS
  • Study the properties of Hermitian and unitary matrices in quantum mechanics
  • Learn about the transformation between Dirac and Chiral representations of gamma matrices
  • Explore techniques for solving matrix equations involving multiple matrices
  • Investigate the significance of ##\gamma_D^5## in the context of Dirac matrices
USEFUL FOR

Physicists, particularly those specializing in quantum mechanics and particle physics, as well as students studying advanced topics in linear algebra and matrix theory.

Akineton
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Hello friends, I'm trying to construct transformation matrix S such that it transforms Dirac representations of gamma matrices into Chiral ones. I know that this S should be hermitian and unitary and from this I arrived an equation with 2 matrices on the LHS (a known matrix multiplied by S from left) and another couple on the RHS (a known matrix multiplied by S from right). In addition, I have same equation with other known matrices. How can I find S from these?

The original question is attached.

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You should post this in the home-work section of these forums! Hint: write out ##\gamma_D^5## in the last equation should be a good starting point.
 

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