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Why are disconnected diagrams dropped from S-Matrix

  1. Jan 20, 2016 #1
    I am talking about perturbative quantum field theory. When calculating elements of correlation functions(which then I use to calculate S-matrix elements) one always comes up with connected and disconnected diagrams. These disconnected diagrams are usually dropped from the calculation and I wonder why. Note that I am not talking about vacuum-vacuum diagrams.
    I'll give an example, suppose you have real scalar field with a Phi^3 interaction AND a Phi^6 interaction. A 2Phi->4Phi particle scattering can happen in at least two ways (as calculated from a six point correlating function):
    One 6-point vertex in which 2 initial particles enter and 4 final particles exit.
    Two 3-point vertex. In each vertex 1 initial particle enters and 2 final particles exit.
    It seems to be tacitly assumed that the second diagram may be dropped. In most cases we may understand these to be two separate processes, but there must be some cases in which the two terms contribute to the same process: there must be quantum interference between the terms.
    Is there some process that kills this interference? Why is the disconnected diagram usually dropped?
  2. jcsd
  3. Jan 20, 2016 #2


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    I am not an expert on this, but I remember that the interferences drop out as you average over the relative temporal/ spatial separation of the scattering events. You finally get a simple product of the averaged S-matrix contribution.
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