Stochastic quantization of para-Fermi fields

Balakrishnan, Janaki ; Biswas, S. N. ; Goyal, Ashok ; Soni, S. K. (1990) Stochastic quantization of para-Fermi fields Journal of Mathematical Physics, 31 (1). pp. 156-163. ISSN 0022-2488

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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.

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