Normal ordering and Wick contraction?

ismaili

Dear all,

I have a formula at hand but I don't know how to derive it.
[tex]: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')\}:[/tex]
where [tex]::[/tex] denotes normal ordering, and [tex]X^\mu(x)[/tex] is the field. [tex]\langle X^\mu(x)X^\nu(x')\rangle[/tex] 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.