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In some quantum field theories tadpoles of the form

                                                            enter image description here

can be attached to a diagram and contribute to the amplitude of a process. Why is any such contribution not generally zero? By momentum conservation at the vertex any momentum flowing through the connecting line must be zero.

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    $\begingroup$ Perhaps I'm blind, but I do not see why the fact that "the momentum flowing thorugh the line must be zero" would imply that the contribution to the amplitude must be zero. $\endgroup$
    – ACuriousMind
    Commented Jun 16, 2015 at 12:41
  • $\begingroup$ I guess it seems like the tadpole might as well not be there if no momentum passes through the tadpole. So perhaps the tadpole ought to have no affect on the amplitude. $\endgroup$
    – innisfree
    Commented Jun 16, 2015 at 12:51
  • $\begingroup$ however there are still Feynman rules associated with the lines, vertices etc in the tadpole $\endgroup$
    – innisfree
    Commented Jun 16, 2015 at 12:52
  • $\begingroup$ @ACuriousMind At the vertex the tadpole interacts with the diagram and changes it somehow from what it would be without it. Now to me it seems that conservation laws forbid any change in momentum, energy, spin, etc. by the tadpole. What is there left for it to change without violating conservation laws? $\endgroup$
    – dan-ros
    Commented Jun 16, 2015 at 13:23
  • $\begingroup$ A tadpole contains a divergent integral over the loop momenta. Despite the fact that the momenta running through the dotted propagator is constrained to be a zero 4-vector. $\endgroup$ Commented Jun 18, 2015 at 0:43

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