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If $n\neq D/2$ then OP's integral is dimensionful (i.e. it has non-zero mass dimension $D-2n\neq 0$ in natural units), but it doesn't depend on any dimensionful parameters, so the only possible consistent answer of the regularization is zero. If $n=D/2$ then OP's integral is logarithmically divergent, and in fact non-zero in dimensional regularization.


3

Consider a generic Feynman diagram with, $L$ loops, $N_f$ number of internal fermion lines (or fermionic propagators) and $N_b$ number of internal boson lines (or bosonic propagators), different kinds of vertices and the $i^{th}$ kind appears $N_{v_i}$ times, and number of derivatives in each vertex be $h_i$. Now suppose that we have written down the ...


2

I think you're looking for one of two things: The Uehling potential which essentially represents the lowest order modification to the electric field between point charges due to quantum fluctuations. A related concept (Also mentioned by @Artem Alexandov) called vacuum polarisation. The quantum vacuum can be thought of as full of virtual electron-positron ...


1

Infrared divergences can arise in various ways. Usually we refer to two sources as most important: External particles with vanishingly small momenta (so called "soft particles"). These are particles, usually photons, that are not observable by detectors in the sense that their momenta are so small that instruments are not sensitive to them. It turns out ...


1

Forget about the RG flow for a moment. Pick a value of $\mu$ so that $\alpha(\mu)$ is small. Now, fixing that small $\alpha$, take a look at a scattering process at high enough energy $M$ so that $\alpha(M)$ would be large (but still use your small $\alpha$). You will find that the 1-loop correction to your scattering process is large compared to the tree ...


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