Normal ordering and Wick contraction?

  1. 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.
  2. jcsd
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