Saturday, 11 October 2014

quantum field theory - phi4 Propagator - Feynman Diagram: internal vertex that loops back to itself


In all that follows I'll be dealing with everything massless.


The free, massless propagator (L=d4x(ϕ(x))2) is supposedly given by G0(x,y)=c(xy)2, where I believe c=14π2.



I'm trying to calculate the propagator in ϕ4-theory, specifically the contribution due to this diagram: enter image description here


Using the Feynman rules in position space, I believe that I should be getting a contribution of the form: C(x1,x2)=iλd4u G0(x1,u)G0(u,u)G0(u,x2)


However, here is my question: why do I get G0(u,u)=c(uu)2=undefined? There's no way I can see to evaluate this integral.


How do I deal with this? Maybe I've got the wrong order of variables? I'm new to these kinds of calculations.




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