Hi. I'm currently reading about (negative frequency) solutions to the Dirac equations which can be written on the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \Psi = ( \sqrt{p \cdot \sigma} \chi, \sqrt{p \cdot \bar{\sigma}} \chi)^T e^{-i p \cdot x}[/tex]

For any two component spinor Chi. But the dot product with the four vector p and the sigma vector is a matrix, so here one is taking the square root of a matrix. What do we mean by that? Or am I interpreting this wrong?

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# Solution to the dirac equation and the square root of a matrix?

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