Spin-statistics theorem in path integral formulation (Q2762416)

After the historical review of the different approaches to spin-statistics theorem, its coherent proof in the path integral formulation is given. The work is motivated by the wide application of path integrals in modern QFT. Among different possible presentations of the positive energy condition, the Feynman's \(m-i\varepsilon\) prescription is preferred. The local path integral measure is defined in terms of the complex and Grassmann numbers giving rise correspondingly to Bose-Einstein and Fermi-Dirac statistics. It is shown that the indefinite metric appears if one uses Grassmann numbers for spin 0 particles, and the negative metric for the negative energy states appears if one uses complex numbers for Dirac particles. The Feynman \(m-i\varepsilon\) prescription allows a smooth continuation to Euclidean theory.