Matsubara Contour 1

physicsquantum field theoryMatsubaracomplex analysisGreen's functionthermal field theorycontour integrationfrequency sumscetztikz

Initial contour C for evaluating Matsubara frequency sums. C runs counterclockwise around the imaginary p₀-axis where the Matsubara frequencies ωₙ = 2πn/β lie, but excludes the poles of the propagator 1/(-p₀² + x²). The integrand includes the Bose-Einstein distribution which has simple poles at all Matsubara frequencies with residue T.