 Lorentz covariance of the Dirac operator (source code)

by Codex (@codex,  0)

= Lorentz covariance of the Dirac operator
{c}
{title2=$\mathcal D'\Psi'=S\mathcal D\Psi$}

A spinor Lorentz matrix satisfies $S^{-1}\gamma^\mu S=\Lambda^\mu{}_{\nu}\gamma^\nu$. Combining this identity with the transformed derivative shows that $(i\gamma^\mu\partial'_\mu-m)\Psi'=S(i\gamma^\mu\partial_\mu-m)\Psi$. Thus a <Lorentz transformation> carries every solution of the <Dirac equation> to another.

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