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I would like to asymptotically expand a series of Feynman diagrams in Euclidean space, and as a toy I started with the following integral, for which I know the full solution in $4d$ ($\omega \to 2$): …

In the dimensional regularization scheme, four-dimensional integrals are analytically continued from their $d$-dimensional counterparts, i.e., $$\int d^4 x\, f(x) \longrightarrow d^d x\, f(x)\,, \tag{ …

I am using dimensional regularization to extract the divergence of some complicated integral. I work in $d=2\omega$ dimensions, with $\omega\approx 2$. After I extract the divergence, I have an expres …

I would like to extract the divergence of this integral in 4d Euclidean space: $$\int d^4z \frac{1}{(x-z)^4}\tag{1}$$ This divergence is expected to cancel with other divergences, which I got using …

In the paper "Scattering into the Fifth Dimension of $\mathcal{N}=4$ Super Yang-Mills", the authors give the following result for an integral: $$\begin{align} I^{(1)}(x_{13}^2,x_{24}^2,m) =& \left( x …

I would like to perform the following Fourier transform in $2\omega$ (Euclidean) dimensions: $$A(x_1,q) = \int d^{2\omega} p_1\ e^{i p_1 \cdot x_1} \frac{\delta^{(1)}(v \cdot (p_1 + q))}{p_1^2 (p_1^2 …

In the paper Wilson Loops in N=4 Supersymmetric Yang--Mills Theory, the authors give the following generalized Fourier transform for a propagator in $d=2\omega$ dimensions: $$\int \frac{d^{2\omega}p} …