using KeldyshContraction@qfields c::Destroy(Classical) q::Destroy(Quantum)
elasctic2boson = -(0.5 * (c^2 + q^2) * c' * q' + 0.5 * c * q * ((c')^2 + (q')^2))
L_int = InteractionLagrangian(elasctic2boson)\[\frac{-1}{2} c c \bar{q} \bar{c} + \frac{-1}{2} q q \bar{q} \bar{c} + \frac{-1}{2} q c \bar{c} \bar{c} + \frac{-1}{2} q c \bar{q} \bar{q}\]
GF = DressedPropagator(L_int, 2)Dressed Propagator:
keldysh: -1//2*Gᴿ(x₁,y₁)*Gᴿ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴷ(y₂,y₂)*Gᴷ(y₁,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴷ(y₂,x₂) + -1//2*Gᴿ(x₁,y₁)*Gᴿ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴷ(y₂,x₂) + -1//1*Gᴷ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴷ(y₂,y₂)*Gᴬ(y₁,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴿ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//2*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴷ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//2*Gᴷ(x₁,y₁)*Gᴬ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴿ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴷ(y₂,y₂)*Gᴷ(y₁,x₂) + -1//2*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴷ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴷ(y₂,x₂) + -1//2*Gᴿ(x₁,y₁)*Gᴬ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₁)*Gᴷ(y₁,y₂)*Gᴷ(y₂,y₂)*Gᴬ(y₂,x₂) + -1//1*Gᴷ(x₁,y₁)*Gᴷ(y₁,y₁)*Gᴬ(y₁,y₂)*Gᴷ(y₂,y₂)*Gᴬ(y₂,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₁)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₂)*Gᴷ(y₂,x₂) + -1//1*Gᴷ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//1*Gᴷ(x₁,y₁)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴷ(y₂,y₂)*Gᴬ(y₁,x₂) + -1//2*Gᴷ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴷ(y₁,y₂)*Gᴿ(y₂,y₁)*Gᴬ(y₂,x₂)
retarded: -1//1*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴷ(y₂,y₂)*Gᴿ(y₁,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₁)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₂)*Gᴿ(y₂,x₂) + -1//2*Gᴿ(x₁,y₁)*Gᴿ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴿ(y₂,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴿ(y₂,x₂) + -1//1*Gᴿ(x₁,y₁)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴷ(y₂,y₂)*Gᴿ(y₁,x₂) + -1//2*Gᴿ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴷ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴿ(y₂,x₂)
advanced: -1//1*Gᴬ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴷ(y₂,y₂)*Gᴬ(y₁,x₂) + -1//1*Gᴬ(x₁,y₁)*Gᴷ(y₁,y₁)*Gᴬ(y₁,y₂)*Gᴷ(y₂,y₂)*Gᴬ(y₂,x₂) + -1//1*Gᴬ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//2*Gᴬ(x₁,y₁)*Gᴬ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴿ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//2*Gᴬ(x₁,y₁)*Gᴷ(y₁,y₂)*Gᴷ(y₁,y₂)*Gᴿ(y₂,y₁)*Gᴬ(y₂,x₂) + -1//1*Gᴬ(x₁,y₁)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴷ(y₂,y₂)*Gᴬ(y₁,x₂)Σ = SelfEnergy(GF, 2)Self Energy:
keldysh: -1//1*Gᴷ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴿ(y₂,y₁) + -1//1*Gᴷ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴬ(y₂,y₁) + -1//2*Gᴷ(y₁,y₂)*Gᴷ(y₁,y₂)*Gᴷ(y₂,y₁) + -1//2*Gᴬ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴷ(y₂,y₁) + -1//2*Gᴿ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)
retarded: -1//1*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴷ(y₂,y₂) + -1//1*Gᴷ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁) + -1//1*Gᴷ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴷ(y₂,y₂) + -1//2*Gᴷ(y₁,y₂)*Gᴷ(y₁,y₂)*Gᴬ(y₂,y₁) + -1//2*Gᴿ(y₁,y₂)*Gᴿ(y₁,y₂)*Gᴬ(y₂,y₁)
advanced: -1//1*Gᴷ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴷ(y₂,y₁) + -1//1*Gᴿ(y₁,y₂)*Gᴷ(y₂,y₁)*Gᴷ(y₂,y₂) + -1//1*Gᴷ(y₁,y₂)*Gᴬ(y₂,y₁)*Gᴷ(y₂,y₂) + -1//2*Gᴬ(y₁,y₂)*Gᴬ(y₁,y₂)*Gᴿ(y₂,y₁) + -1//2*Gᴷ(y₁,y₂)*Gᴷ(y₁,y₂)*Gᴿ(y₂,y₁)Σk = wigner_transform(Σ)Self Energy:
keldysh: -1//1*Gᴷ(q₁)*Gᴬ(q₂)*Gᴿ(q₁ + q₂ - k) + -1//1*Gᴷ(q₁)*Gᴿ(q₂)*Gᴬ(q₁ + q₂ - k) + -1//2*Gᴷ(q₁)*Gᴷ(q₂)*Gᴷ(q₁ + q₂ - k) + -1//2*Gᴬ(q₁)*Gᴬ(q₂)*Gᴷ(q₁ + q₂ - k) + -1//2*Gᴿ(q₁)*Gᴿ(q₂)*Gᴷ(q₁ + q₂ - k)
retarded: -1//1*Gᴿ(q₁)*Gᴷ(q₁)*Gᴷ(q₃) + -1//1*Gᴷ(q₁)*Gᴿ(q₂)*Gᴷ(q₁ + q₂ - k) + -1//1*Gᴷ(q₁)*Gᴬ(q₁)*Gᴷ(q₃) + -1//2*Gᴷ(q₁)*Gᴷ(q₂)*Gᴬ(q₁ + q₂ - k) + -1//2*Gᴿ(q₁)*Gᴿ(q₂)*Gᴬ(q₁ + q₂ - k)
advanced: -1//1*Gᴷ(q₁)*Gᴬ(q₂)*Gᴷ(q₁ + q₂ - k) + -1//1*Gᴿ(q₁)*Gᴷ(q₁)*Gᴷ(q₃) + -1//1*Gᴷ(q₁)*Gᴬ(q₁)*Gᴷ(q₃) + -1//2*Gᴬ(q₁)*Gᴬ(q₂)*Gᴿ(q₁ + q₂ - k) + -1//2*Gᴷ(q₁)*Gᴷ(q₂)*Gᴿ(q₁ + q₂ - k)ci = KeldyshContraction.CollisionIntegral(Σk)
ci.terms[[3]]-1//8*F(k)*F(q₁)*F(q₂) + -1//4*F(q₁ + q₂ - k) + 1//2*F(q₁) + 1//4*F(k)*F(q₁)*F(q₁ + q₂ - k) + -1//16*F(q₁)*F(q₂)*F(q₁ + q₂ - k) + -1//8*F(k)This page was generated using Literate.jl.