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I've been looking at the Klein Gordon equation, Maxwell's equation, and the Dirac equation in curved space and I was wondering if there is an underlying formalism regarding how to derive them from their flat space counterparts.

What I mean is, at the heart of the whole process for all spins is the switching from normal derivatives to covariant derivatives. However, in the Dirac case most people apply the tetrad formalism of transforming to a locally flat frame: why isn't this done in the other cases? (is it just that there is an easier way?)

Is it not possible to take the Dirac Lagrangian, switch round the derivatives accordingly as you would with the spin-0 Lagrangian, and derive the wave equations that way?

Hope this made sense!

-FD

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# Quantum wave equations in curved space

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