Undergrad Transformation matrix from Dirac to Weyl

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To construct the transformation matrix S that converts Dirac representations of gamma matrices to Chiral ones, it is essential that S is both Hermitian and unitary. The user has derived an equation involving known matrices on both sides, which includes S. To solve for S, it is suggested to express the gamma matrix ##\gamma_D^5## in the last equation as a starting point. This approach may help in isolating S and finding a solution. Overall, the focus is on deriving S through careful manipulation of the equations involving the gamma matrices.
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?

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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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