How I derive the Dyson-Schwinger equations for
the electron propagator S(p),
S(p)=S0(p)+S0(p)∗(e2∫d4k(2π)4γμDμν(p−k)S(k)Γν(p,k))∗S(p),
the photon propagator Dμν(p)
Dμν(p)=Dμν0(p)+Dμν′0(p)∗(−e2tr[∫d4k(2π)4γν′S(k)Γμ′(k,k+p)S(k+p)])∗Dμ′ν(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(−i∂J)∂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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