# Normal ordering and Wick contraction?

1. Jul 12, 2008

### ismaili

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.