International Journal of Theoretical Physics

, Volume 58, Issue 4, pp 1150–1156 | Cite as

Stochastic Quantization of Massive Fermions

  • A. N. EfremovEmail author


We consider a general solution of the Langevin equation describing massive fermions to an appropriate boundary problem. Assuming existence of such solution we show that its correlators coincide with the Schwinger functions of corresponding Euclidean Quantum Field Theory.


Stochastic quantization Fermions Langevin equation 



I thank the Institute for Theoretical Physics at the University of Leipzig, Germany for the financial support.


  1. 1.
    Kupiainen, A.: Renormalization group and stochastic PDE’s. Annales Henri Poincaré 17, 497–535 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Hairer, M.: Introduction to regularity structures. Braz. J. Probab. Stat. 29, 175–210 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Glimm, J.: The Yukawa coupling of quantum fields in two dimensions. II. Commun. Math. Phys. 6(1), 61–76 (1967)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gross, D.J., Neveu, A.: Dynamical symmetry breaking in asymptotically free field theories. Phys. Rev. D 10, 3235–3253 (1974)ADSCrossRefGoogle Scholar
  5. 5.
    Wilson, K.G.: Renormalization group and critical phenomena. Phys. Rev. B 4 (9), 3174–3183 (1971)ADSCrossRefzbMATHGoogle Scholar
  6. 6.
    Parisi, G., Wu, Y.: Perturbation theory without gauge fixing. Sci. Sin. 24, 483 (1981)MathSciNetGoogle Scholar
  7. 7.
    Berezin, F.A.: Introduction to Superanalysis. Springer (1987)Google Scholar
  8. 8.
    Damgaard, P.H., Hüffel, H.: Stochastic quantization. Phys. Rep. 152(5), 227–398 (1987)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Zinn-Justin, J.: Renormalization and stochastic quantization. Nucl. Phys. B275, 135–159 (1986)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Osterwalder, K.: Euclidean Fermi Fields, pp. 326–331. Springer, Berlin (1973)Google Scholar
  11. 11.
    Glimm, J., Jaffe, A.: Quantum Physics. Springer (1987)Google Scholar
  12. 12.
    Osterwalder, K., Schrader, R.: Feynman-kac formula for euclidean fermi and bose fields. Phys. Rev. Lett. 29, 1423–1425 (1972)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.CPHT, Ecole Polytechnique, CNRSUniversité Paris-SaclayPalaiseauFrance

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