  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 statistics. The Feynman's
$m-i\epsilon$ prescription ensures the positive energy condition regardless of
statistics, and the abnormal spin-statistics relation for both of spin-0 scalar
particles and spin-1/2 Dirac particles is excluded if one imposes the positive
norm condition in conjunction with Schwinger's action principle. The minus
commutation 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 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 4-dimensional theory but also in 2-dimensional theory.

High Energy Physics - Theory;High Energy Physics - Phenomenology