Dyson-Schwinger Equation

Full Propagator · Self-Energy · Spectral Function A(ω)

Parameters

Dyson Equation

G(ω) = 1/(ω² − m₀² − Σ(ω))
Σ(ω) = −iλ² G(ω) (tadpole)
A(ω) = −(1/π) Im G(ω+iε)
Self-consistent solution...

Theory

Dyson's equation resums all 1PI diagrams into the self-energy Σ. The dressed propagator G=(G₀⁻¹−Σ)⁻¹ encodes mass renormalization (Re Σ shifts the pole) and damping (Im Σ gives finite width). The spectral function A(ω) satisfies the sum rule ∫A dω=1 (unitarity). Self-consistent (Dyson-Schwinger) approach goes beyond perturbation theory.