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I would like to know if there is any easy way to perform the operator product expansion of the following

$:\partial X^{\mu}\bar{\partial}X^{\nu}e^{ik_{\rho}X^{\rho}}(z,\bar{z})::\partial X^{\alpha}\bar{\partial}X^{\beta}e^{ik_{\sigma}X^{\sigma}}(w,\bar{w}):$

I tried to find all the contraction terms and use wick's theorem, but it turns out to be a mission impossible. How to compute it quickly?

Check the 2nd chapter of Polchinski. All the necessary techniques are given there.

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