Issues

 / 

1972

 / 

February

  

Reviews of topical problems


Use of Functional Integrals in Quantum Mechanics and Field Theory

Physicists are becoming more interested in solving the equations of quantum theory without using methods requiring expansion in powers of the interaction constant. The perturbation-theory method, which gave results that agree splendidly with experiment in quantum electrodynamics, turned to be inapplicable in strong-interaction theory. One of the methods in which a radical attempt is made to go beyond the framework of perturbation theory, is the method of functional integration in quantum theory, first proposed by Feynman. The present review, which is devoted to this method, introduces in lucid fashion the concepts of functional integrations and then explains some applications of this method in quantum field theory. Much attention is paid to the use of functional integrals in infrared and high-energy asymptotic relations in field theory. The review does not claim an exposition of the mathematical difficulties connected with the concept of functional integral, and focuses attention to certain successes in its use in quantum physics.

PACS: 03.65.Db, 11.10.Ef, 03.65.Ca, 11.10.Cd, 02.30.Rz (all)
DOI: 10.1070/PU1972v015n02ABEH004963
URL: https://ufn.ru/en/articles/1972/2/e/
Citation: Blokhintsev D I, Barbashov B M "Use of Functional Integrals in Quantum Mechanics and Field Theory" Sov. Phys. Usp. 15 193–204 (1972)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Блохинцев Д И, Барбашов Б М «Применения функциональных интегралов в квантовой механике и теории поля» УФН 106 593–616 (1972); DOI: 10.3367/UFNr.0106.197204b.0593

Cited by (19) Similar articles (20) ↓

  1. V.I. Ogievetskii, L. Mezincescu “Boson-fermion symmetries and superfields18 960–982 (1975)
  2. A.I. Alekseev “The application of the methods of quantum field theory in statistical physics4 23–50 (1961)
  3. D.I. Blokhintsev, V.S. Barashenkov, B.M. Barbashov “The structure of nucleons2 505–525 (1959)
  4. F.A. Berezin “Feynman path integrals in a phase space23 763–788 (1980)
  5. D.N. Zubarev “Double-time Green functions in statistical physics3 320–345 (1960)
  6. L.D. Faddeev, V.N. Popov “Covariant quantization of the gravitational field16 777–788 (1974)
  7. Ya.A. Smorodinskii, A.L. Shelepin, L.A. Shelepin “Groups and probabilities at the foundations of quantum mechanics35 (12) 1005–1051 (1992)
  8. B.M. Barbashov, V.V. Nesterenko “Superstrings: a new approach to a unified theory of fundamental interactions29 1077–1096 (1986)
  9. M.K. Volkov, V.N. Pervushin “Quantum field theory with a chiral Lagrangian and low-energy meson physics19 894–908 (1976)
  10. A.M. Dykhne, G.L. Yudin “’Jarring’ of a quantum system and the corresponding stimulated transitions21 549–565 (1978)
  11. V.B. Adamskii “Local invariance and the theory of compensating fields4 607–616 (1962)
  12. V.I. Tatarskii “The Wigner representation of quantum mechanics26 311–327 (1983)
  13. D.I. Blokhintsev “Interaction of a microsystem with a measuring instrument11 320–327 (1968)
  14. B.I. Spasskii, A.V. Moskovskii “Nonlocality in quantum physics27 273–283 (1984)
  15. D.I. Blokhintsev “Basis for special relativity theory provided by experiments in high energy physics9 405–413 (1966)
  16. D.I. Blokhintsev “High-energy physics and the fundamental principles of modern theory8 612–613 (1966)
  17. L.V. Prokhorov, S.V. Shabanov “Phase space of mechanical systems with a gauge group34 (2) 108–140 (1991)
  18. F.V. Bunkin, A.E. Kazakov, M.V. Fedorov “Interaction of intense optical radiation with free electrons (nonrelativistic case)15 416–435 (1973)
  19. V.Ya. Fainberg “Theoretical foundations of the CPT theorem11 506–511 (1969)
  20. S.G. Suvorov “On certain gnoseological problems in physics12 359–377 (1969)

The list is formed automatically.

© 1918–2023 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions