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This is a problem that I met in real-life physics research. This question is related to Wick's theorem. The question is:

1. In two dimensional plane with polar axis, why do we have the following relation: $\int e^{i\bf{p}\cdot \bf{a}}/p^4 \space d^2p = C \space R^2 (\ln(R))^2 $, where $C$ is a constant, $ \bf{a}$ is a vector and $R = |\bf{a}|$.

  1. Moreover, how do we calculate the following:

$\int e^{i\bf{p}\cdot \bf{a}}/(p^4 + C_1 p^2) $

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