Monday, 20 April 2015

homework and exercises - How to get Dyson-Schwinger equations for quantum electrodynamics?



How I derive the Dyson-Schwinger equations for


the electron propagator S(p),


S(p)=S0(p)+S0(p)(e2d4k(2π)4γμDμν(pk)S(k)Γν(p,k))S(p),


the photon propagator Dμν(p)


Dμν(p)=Dμν0(p)+Dμν0(p)(e2tr[d4k(2π)4γνS(k)Γμ(k,k+p)S(k+p)])Dμν(p), and the electron-photon-vertex' Γν(p,p)


Γν(p,p)=Γν0(p,p)+d4k(2π)4S(p+k)Γν(p+k,p+k)S(p+k)K(p+k,p+k,k).


???


I have no idea, because the definition of the Dyson-Schwinger equation


(S(iJ)ϕ+J)Z(J)=0


seems to be completely different to the equations above. What I have to do to obtain these equations? Is there a way to derive these equations?





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