Hi, I had a silly idea that probably doesn't work, but I thought I'd ask about it anyway.(adsbygoogle = window.adsbygoogle || []).push({});

I understand that vectors can be thought of as derivative operators, e.g. [itex]\frac{d}{d\lambda} = \frac{dx^\mu}{d\lambda} \partial_\mu[/itex], where lambda parametrizes some curve.

I also gather that one-forms are linear maps from the tangent space to the real numbers, i.e. they 'eat' a vector and 'spit out' a real number. But surely the ideal thing to take a derivative operator and spit out a real number is an (indefinite) integral operator? Something like

[tex]\int^x d\lambda \frac{d}{d\lambda} f(\lambda) = f(x)[/tex]

The reason I'm not sure this works is because differential forms are supposed to be the ideal thing to integrate themselves, and I'm not sure an integral operator works as something to integrate. Then again a derivative operator isn't something you can differentiate (you can apply them multiple times but that is different), but you can still get the divergence and curl of vector fields...

I feel like it ought to work because the integral operator is obiously the inverse of the derivative operator!

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# Differential forms as antiderivatives?

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