# Normal ordering and Wick contraction?

by ismaili
Tags: contraction, normal, ordering, wick
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 P: 161 Dear all, I have a formula at hand but I don't know how to derive it. $$:e^{ik\cdot X(x)}::e^{ik'\cdot X(x')}: = \exp\{-k_\mu k'_\nu\langle X^\mu(x)X^\nu(x')\rangle\} :\exp\{ik\cdot X(x)+ik'\cdot X(x')\}:$$ where $$::$$ denotes normal ordering, and $$X^\mu(x)$$ is the field. $$\langle X^\mu(x)X^\nu(x')\rangle$$ is the propagator. I met this problem in the study of vertex operators of string theory. I think this is a field theory stuff but I just can't derive it. Any help will be appreciated.

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