# $d$-dimensional Fourier integral of log term

+ 1 like - 0 dislike
114 views

I was wondering if there exists a general formula for Fourier transform integrals of this type, which appear frequently in qft

$$\int \frac{d^d k}{(2\pi)^d} \, e^{i\vec{k}\cdot \vec{x}} [\log k^2]^n [k^2]^m,$$
where the metric is euclidean.
I know a general formula that holds in dimensional regularization for the same integrals without the log term, or for the integral with $n=1, m=0$, but I cannot find anything similar for the integral above.. Does anyone know if these integrals can be regularized and have a closed expression? Even something for a fixed dimension $d$ would be cool.

Thank you so much!

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysics$\varnothing$verflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.