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Normal ordering and Wick contraction? 
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#1
Jul1208, 10:07 PM

P: 161

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. 


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