Stochastic quantization of order two parafermi fields

The method of stochastic quantization of Parisi–Wu is extended to include spinor fields obeying the generalized statistics of order two consistent with the weak locality requirement. Appropriate Langevin and Fokker–Planck equations are constructed using paragrassmann variables, which give rise to two fields with different masses in the equilibrium limit, in agreement with the results of the canonical quantization procedure. The connection between the stochastic quantization method and conventional Euclidean field theory is established through Klein transformations. Received: 14 November 2001 / Published online: 8 February 2002