Matsubara Contour 4

physicsquantum field theoryMatsubaracomplex analysisGreen's functionthermal field theorycontour integrationfrequency sumscetztikz

Special contour Cᵦ used to isolate branch cut contributions in Matsubara frequency sums. The contour runs along both sides of the real axis where the sign function s(p₀) changes discontinuously, giving rise to branch cuts in the propagator. This allows separating pole and branch cut contributions.