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Dirac equation in curved spacetime is given by $$\left(i \gamma^\mu D_\mu-m\right) \Psi=0$$

How does we know that this is the correct equations to describe spinors in curved space time? Is there any expriment that comprove that this is the correct equation?

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    $\begingroup$ 'Correctness' is undefinable in physics. Rather, you must at least ensure that an equation 1) respects certain symmetries and 2) reduces to an empirically tested theory at low energies. It's then essentially up to new experiments to verify the numbers provided by the equation. See also physics.stackexchange.com/a/727992/133418 $\endgroup$
    – Avantgarde
    Commented Jul 28, 2023 at 20:37

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