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 Lagrangian, when combined with Green's functions defined in terms of time ordered products, ensure causality regardless of statisitcs. The Feynman's m - i{\epsilon} prescription ensure the positive energy condition regardless of statistics, and and the abnormal spin-statistics relation for both of spin-0 scalar particles and spin-1/2 Dirac particles is excluded if one impose the positive norm condition in conjunction with Schwinger's action principle. The minus comutation relation between one Bose and one Fermi field arises naturally in path integral. The Feynman's m - i{\epsilon} prescription also ensures a smooth continuation to Euclidian 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 4-dimensional theory but also in 2-dimensional theory.