Stochastic quantization of para-Fermi fields

Abstract

The application of the method of stochastic quantization originally attributed to Parisi and Wu has been extended to spinor fields obeying para-Fermi statistics. The connection between Euclidean and stochastic field theories is established in the conventional manner by proving the equivalence between a Langevin equation satisfied by para-Grassmann fields and a Fokker–Planck equation, the Hamiltonian of which has been constructed using para-Grassmann variables analogous to its construction from Grassmann variables in the Fermi case. As an example, a two-point Green function is calculated for any arbitrary value of order p of para-Fermi statistics, barring the pathological case p=2 which has been mentioned briefly.