Abstract
The concept of nonlocality is introduced into physics by means of a stochastic context using Langevin and Schwinger-Dyson techniques. This allows us to reformulate the finite theory of quantum fields, free from ultraviolet divergences, based on the stochastic quantization method with nonlocal regulators. As a nonlocal regulator we choose any entire analytic function in the momentum space, which guarantees that our regularization method for any theory of interest does not violate basic physical principles such as unitarity, causality, and gauge invariance of the theory. Here we present the regularization scheme for scalar, gauge, and scalar electrodynamic theories. Our mathematical prescription is similar to the continuum regularization method of quantum field theory with meromorphic regulators investigated by Bern and his team.
Similar content being viewed by others
References
Alfaro, J., and Sakita, B. (1983).Physics Letters,121B, 339.
Batrouni, G. G.,et al. (1985).Physical Review D,32, 2736.
Bern, Z. (1985).Nuclear Physics B,251, 633.
Bern, Z., and Chan, H. S. (1986).Nuclear Physics B,266, 509.
Bern, Z.,et al. (1987a).Nuclear Physics B,284, 1.
Bern, Z.,et al. (1987b).Nuclear Physics B,284, 35.
Bern, Z.,et al. (1987c).Nuclear Physics B,284, 92.
Breit, J. D., Gupta, S., and Zaks, A. (1984).Nuclear Physics B,233, 61.
Chaichian, M., and Nelipa, N. F. (1984).Introduction to Gauge Field Theories, Springer-Verlag, Berlin.
Claudson, M., and Halpern, M. B. (1985).Physical Review D,31, 3310.
Damgaard, R., and Huffel, H. (1987).Stochastic Quantization, World Scientific, Singapore.
Doering, C. R. (1985).Physical Review D,10, 2445.
Efimov, G. V. (1977).Nonlocal Interactions of Quantized Fields, Nauka, Moscow.
Efimov, G. V. (1985).Problems of Nonlocal Quantum Field Theory, Energo-Izdatelstvo, Moscow.
Floratos, E. G.,et al. (1984).Nuclear Physics B,241, 221.
Furlan, G., Jengo, R., Pati, J., and Sciama, D. (eds.) (1987).Superstrings, Unified Theories and Cosmology, World Scientific, Singapore.
Green, M. B., Schwarz, J. H., and Witten, E. (1987).Superstring Theory, Cambridge University Press, Cambridge.
Greensite, J., and Halpern, M. B. (1983).Nuclear Physics B,211, 343.
Greensite, J., and Halpern, M. B. (1984).Nuclear Physics B,242, 167.
Guerra, F. (1981). Structural aspects of stochastic mechanics and stochastic field theory,Physics Reports C,77, 263–312.
Hamber, H. W., and Heller, U. M. (1984).Physical Review D,29, 928.
Lai, C. H. (ed.). (1983).Gauge Theory of Weak and Electromagnetic Interactions (Selected Papers), World Scientific, Singapore.
Migdal, A. A. (1986). Stochastic quantization of field theory,Uspekhi Fizicheskikh Nauk,149, 3–45 (in Russian).
Namiki, M., and Yamanaka, Y. (1984).Hadronic Journal,7, 594.
Namsrai, Kh. (1986).Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics, D. Reidel, Dordrecht, Holland.
Nelson, E. (1967).Dynamical Theories of Brownian Motion, Princeton University Press. Princeton, New Jersey.
Niemi, A. J., and Wijewardhana, L. C. R. (1982).Annals of Physics (N.Y.),140, 247.
Papp, E. (1975).International Journal of Theoretical Physics,15, 735.
Parisi, G., and Wu, Y. S. (1981).Scientifica Sinica,24, 483.
Wali, K. (ed.) (1987).Proceedings on the Eighth Workshop on Grand Unification, World Scientific, Singapore.
Zwanziger, D. (1981).Nuclear Physics B,192, 259.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dineykhan, M., Namsrai, K. Nonlocality and stochastic quantization of field theory. Int J Theor Phys 28, 719–763 (1989). https://doi.org/10.1007/BF00669819
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00669819