Skip to main content
SpringerLink
Log in

Dynamics of spontaneous chiral symmetry breaking and the continuum limit in quantum electrodynamics

Динамика спонтанного нарущения киральной симметрии и непрерывной предел в квантовой злектродинамике

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

The phase diagram in the coupling constant in QED and its connection with the spontaneous chiral symmetry breaking are discussed. The mechanism of such a breaking connected with the collapse phenomenon is considered and a simple physical interpretation of the recent results of the computer simulations in lattice QED is given. The problem of the existence of the nontrivial continuum QED is analysed and, as a result, the following hypothesis is considered: in the Landau-Pomeranchuk-Fradkin « zero-charge » situation (the renormalization constantZ 3=0) theS-matrix of continuum QED with a fixed bare coupling constant,α (0)=α c∼1, is nontrivial. The physical content of such a hypothetical continuum theory is revealed.

Riassunto

Si discutono il diagramma di fase nella costante di accoppiamento in QED e la sua connessione con la rottura di simmetria chirale spontanea. Si considera il meccanismo di questa rottura connesso con il fenomeno di collasso e si fornisce una semplice interpretazione fisica dei risultati recenti delle simulazioni con il calcolatore nel QED del reticolo. Si analizza il problema dell’esistenza della QED non banale nel continuo e, come risultato, si considera l’ipotesi seguente: nella situazione «a carica zero» di Landau-Pomeranchuk-Fradkin (la costante di rinormalizzazioneZ 3=0) la matriceS della QED nel continuo con una costante di accoppiamento nuda fissata,α (0)=α c∼1 è non banale. Si rivela il contenuto fisico di questa teoria ipotetica nel continuo.

Реэюме

Обсуждается фаэовая диаграмма по константе свяэи в квантовой злектродинамике и ее свяэь со спонтанным нарущением киральной симметрии. Рассматривается механиэм такого нарущения, свяэанный с явлением коллапса. Предлагается простая фиэическая интерпретация недавних реэультатов моделирования на ЭВМ в рамках квантовой злектродинамики на рещетке. Аналиэируется проблема сушествования нетривиальной непрерывной квантовой злектродинамики. Рассматривается следуюшая гипотеэа: в случае « нулевого эаряда » Ландау-Поме-ранчук а-Фрадкина (постоянная перенормировкиZ 3=0)S-матрица непрерывной кван?товой злектродинамики с фиксированной голой постоянной свяэи,α (0)=α c∼1, является нетривиальной. Аналиэируется фиэический смысл такой гипотетической непрерывной теории.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Bartholomew, J. Kogut, S. H. Shenker, J. Sloan, M. Stone, H. W. Wyld, J. Shigmetsu andD. K. Sinclair:Nucl. Phys. B,230, 222 (1984).

    Article  ADS  Google Scholar 

  2. M. Gell-Mann andF. Low:Phys. Rev.,95, 1300 (1954).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. L. D. Landau andI. Ya. Pomeranchuk:Dokl. Akad. Nauk SSSR,102, 489 (1955);L. D. Landau: inNiels Bohr and the Development of Physics, edited byW. Pauli (Pergamon Press, London, 1955).

    MathSciNet  MATH  Google Scholar 

  4. E. S. Fradkin:Ž. Ėksp. Teor. Fiz.,28, 750 (1955).

    MathSciNet  Google Scholar 

  5. K. Johnson, M. Baker andR. Willey:Phys. Rev. B,136, 1111 (1964);S. L. Adler:Phys. Rev. D,5, 3021 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  6. N. V. Krasnikov:Phys. Lett. B,126, 483 (1983);Y. Matsubara, T. Suzuki andI. Yotsuyanagi: preprint DPKU-8304, Kanazawa (1983).

    Article  MathSciNet  ADS  Google Scholar 

  7. V. A. Miransky:Phys. Lett. B,91, 421 (1980); preprint ITP-81-22E, Kiev (1981).

    Article  ADS  Google Scholar 

  8. P. I. Fomin andV. A. Miransky:Phys. Lett. B,64, 166 (1976).

    Article  ADS  Google Scholar 

  9. P. I. Fomin, V. P. Gusynin andV. A. Miransky:Phys. Lett. B,78, 136 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  10. P. I. Fomin, V. P. Gusynin, V. A. Miransky andYu. A. Sitenko:Riv. Nuovo Cimento,6, No. 5 (1983).

    Google Scholar 

  11. G. J. Ni:Nucl. Phys. B,211, 414 (1983).

    Article  ADS  Google Scholar 

  12. W. A. Bardeen, M. Moshe andM. Bander:Phys. Rev. Lett.,52, 1188 (1984);M. B. Halpern:Phys. Lett. B,137, 382 (1984).

    Article  ADS  Google Scholar 

  13. In other words, in the relativistic theory the « fall into the centre » (collapse) phenomenon (13,14) takes place for this potential and such a system has no ground state. The formal (mathematical) reason for this phenomenon is connected with the fact that such a Hamiltonian is a Hermitian but not a self-adjoint operator, and it should be extended (defined completely) to become a self-adjoint one (15). The physical reason is connected with the fact that the properties of the system depend on the way used to define completely the Hamiltonian at small distances.

  14. Ya. B. Zel’dovich andV. S. Popov:Usp. Fiz. Nauk,105, 403 (1971);J. Rafelski, L. Fulcher andA. Klein:Phys. Rep.,38, 229 (1978).

    Article  MATH  Google Scholar 

  15. L. D. Landau andE. M. Lifshits:Quantum Mechanics (Nauka, Moscow, 1974), Chapt. 35.

    Google Scholar 

  16. M. Reed andB. Simon:Methods of Modern Mathematical Physics (Academic Press, New York, N. Y., 1975), Vol.2.

    MATH  Google Scholar 

  17. The appearance of such quasi-stationary levels is interpreted as instability with respect to the spontaneous creation of electron-positron pairs from the vacuum (13). The created electron is coupled to the centre thus shielding the charge of the latter while the positron goes to infinity; the process is repeated until the charge of the centre is reduced to a subcritical value.

    Article  Google Scholar 

  18. The role of the fermion mass in the problem of the supercritical Coulomb field can be seen from eqs. (4) and (5). The imaginary part of the energy Imɛ (n) decreases (i.e. stability of the system increases) with increasing mass. Thus there are in principle two possibilities for the system with the supercritical charge to become stable: to shield spontaneously the charge or to generate spontaneously the fermion mass. In the problem of the Coulomb centre the first possibility can be only realized (which is already due to the formulation of the problem as a one-particle one). It has been suggested in ref. (8) that the second possibility—dynamical generation of the fermion mass—is realized in QED.

    Article  ADS  Google Scholar 

  19. H. Bateman andA. Erdélyi:Higher Transcendental Functions, Vol.1 (McGraw-Hill, New York, N. Y., 1953).

    Google Scholar 

  20. B. M. McCoy andT. T. Wu:Phys. Lett.,87, 50 (1979).

    Article  Google Scholar 

  21. S. Coleman:Phys. Rev. D,11, 2088 (1975).

    Article  ADS  Google Scholar 

  22. S. L. Adler:Phys. Rev.,177, 2426 (1969);J. S. Bell andR. Jackiw:Nuovo Cimento A,60, 47 (1969).

    Article  ADS  Google Scholar 

  23. Th. A. J. Maris, G. Jacob andB. Liberman:Nuovo Cimento A,52, 116 (1967);H. Pagels:Phys. Rev. D,7, 3689 (1973).

    Article  ADS  Google Scholar 

  24. S. Goldstein:Phys. Rev.,91, 1516 (1953).

    Article  ADS  MATH  Google Scholar 

  25. S. L. Adler andW. A. Bardeen:Phys. Rev. D,4, 3045 (1971).

    Article  ADS  Google Scholar 

  26. Note that taking into account condition (14) in the case of quantum chromodynamics it is possible to determine uniquely the ultraviolet asymptotics of the dynamical quark mass function directly from the equations for Green’s functions without using the assumption of the validity of operator product expansion (23).

  27. V. A. Miransky:Yad. Fiz.,38, 468 (1983).

    Google Scholar 

  28. V. A. Miransky, V. P. Gusynin andYu. A. Sitenko:Phys. Lett. B,100, 157 (1981).

    Article  ADS  Google Scholar 

  29. S. Mandelstam:Nucl. Phys. B,213, 149 (1983);L. Brink, O. Lingren andB. Nilsson:Phys. Lett. B,123, 323 (1983);P. Howe, K. S. Stelle andP. Townsend:Nucl. Phys. B,214, 519 (1983);S. Fubini andE. Rabinovici: preprint TH. 3825-CERN (1984).

    Article  MathSciNet  ADS  Google Scholar 

  30. InProceedings of the XVIII Solvay Conference on Physics, edited byL. Van Hove,Phys. Rep.,104, 201 (1984).

  31. V. de Alfaro, S. Fubini, G. Furlan andC. Rossetti:Currents in Hadron Physics (North-Holland, Amsterdam, 1973).

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, 252130, Kiev-130, USSR

    V. A. Miransky

Authors
  1. V. A. Miransky
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

To speed up publication, the author of this paper has agreed to not receive the proofs for correction.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miransky, V.A. Dynamics of spontaneous chiral symmetry breaking and the continuum limit in quantum electrodynamics. Nuov Cim A 90, 149–170 (1985). https://doi.org/10.1007/BF02724229

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02724229

PACS

Search

Navigation