Spin-statistics theorem in path integral formulation

We present a coherent proof of the spin-statistics theorem in path integral formulation. The local path integral measure and Lorentz-invariant local L agrangian, when combined with the Green functions defined in terms of time ordered products, ensure causality regardless of statistics. The Feynman m - i epsilon prescription ensures the positive energy condition regardless o f statistics, and the abnormal spin-statistics relation for both the spin-0 scalar particles and spin-1/2 Dirac particles is excluded if one imposes t he positive norm condition in conjunction with Schwinger's action principle . The minus commutation relation between one Bose and one Fermi field arise s naturally in the path integral. The Feynman m - i epsilon prescription al so ensures a smooth continuation to Euclidean theory, for which the use of the Weyl anomaly is illustrated to exclude the abnormal statistics for the scalar and Dirac particles not only in four-dimensional theory but also in two-dimensional theory.