# Quantum Field Theory in position space instead of momentum space?

What are the reasons why we usually treat Quantum Field Theory in momentum space instead of position space? Are the computations (e.g. of Feynman diagrams) generally easier and are there other advantages of this formulation?

• I believe it's just because we can take the $\partial_\mu$ of spacetime and replace it with a momentum $p_\mu$, no? In other words it's the same reason that anyone does anything in $k$-space. – CR Drost Dec 20 '16 at 15:18
• There are plenty of resources at least briefly discussing Feynman diagrams in momentum space. Have you tried googling for e.g. "position space Feynman diagram"? – ACuriousMind Dec 20 '16 at 15:18
• I think it should be made clearer by specific examples, because I saw about four different QFT lecture styles and all of them accented the use of momentum space at different points and for different purposes. – Void Dec 20 '16 at 15:32
• You should still be mindful of position space diagrams. Think about boundaries etc ways translation gets destroyed. – AHusain Dec 21 '16 at 12:08

I may add that the expressions for propagators $G(x,x^{\prime})\propto \int \frac{\mathrm{d}^D k}{k^2+m^2} \mathrm{e}^{-\mathrm{i}k (x-x^{\prime})}$ are quite cumbersome in the position space, and have a plenty of singularities. See, for example, this Wiki article.