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As shown here

http://en.wikipedia.org/wiki/Klein–Gordon_equation#Gravitational_interaction

one can modify the derivative operator in the Minkowski Klein-Gordon equation to generate the GR case for an arbitrary metric.

My question is, what would the quantum current density j be in this case? Given here

http://en.wikipedia.org/wiki/Four-current

is the classical current density in the EM case but that's not really what i'm after.

Furthermore, if i generate a radial wave equation from the GR KG equation in some metric and transform it in a Schrodinger like form, can I just use the standard tools of non-rel QM and use [itex] \psi^* \frac{d}{dx} \psi [/itex] for j?

Cheers!

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# Quantum current density in general relativity

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