Skip to main content
SpringerLink
Log in

Non-abelian gauge theories and triangle anomalies

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

Summary

Conditions for the validity of (a weak version of) the Adler-Bardeen theorem for non-Abelian gauge theories are obtained. Its validity ensures that those theories in which the coefficient of the triangle anomaly vanishes at the one-loop level are anomaly free and therefore they are renormalizable and unitary. This result is based on the derivation of Slavnov-Taylor identities modified by the presence of anomalous terms and on a renormalization-group-like equation for the anomaly coefficient. In the derivation, the dimensional regularization scheme has been followed.

Riassunto

Si presentano le condizioni per la validità di una versione debole del teorema di Adler-Bardeen per teorie di gauge non abeliane. La sua validità assicura che quelle teorie in cui il coefficiente dell’anomalia triangolare si annulla a livello di un’ansa sono libere di anomalie e quindi sono rinormalizzabili ed unitarie. Tale risultato si basa sulla derivazione di identità di Slavnov-Taylor modificate dalla presenza di anomalie e su un’equazione tipo gruppo di rinormalizzazione per il coefficiente dell’anomalia nell’ambito della regolarizzazione dimensionale.

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

Reference

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

    Article  ADS  Google Scholar 

  2. D. Gross andR. Jackiw:Phys. Rev. D,6, 477 (1972).

    Article  ADS  Google Scholar 

  3. H. Georgi andS. L. Glashow:Phys. Rev. D,6, 429 (1972).

    Article  ADS  Google Scholar 

  4. S. L. Adler andW. A. Bardeen:Phys. Rev.,182, 1517 (1969).

    Article  ADS  Google Scholar 

  5. For the extension of the AB theorem toexternal axial current in unbroken non-Abelian gauge theories seeS. Pi andS. S. Shei:Phys. Rev. D,11, 2946 (1975).

    Article  ADS  Google Scholar 

  6. S. Weinberg:Phys. Rev. Lett.,19, 1264 (1967);A. Salam: inElementary Particle Theory, edited byN. Svartholm (Stockholm, 1968).

    Article  ADS  Google Scholar 

  7. A. Slavnov:Theor. Math. Phys.,13, 174 (1972);J. C. Taylor:Nucl. Phys.,33 B, 436 (1971).

    Article  Google Scholar 

  8. For similar equations in QED and in theσ-model seeA. Zee:Phys. Rev. Lett.,29, 1198 (1972);J. H. Lowenstein andB. Shroer:Phys. Rev. D,7, 1929 (1973);S. S. Shei andA. Zee:Phys. Rev. D,8, 597 (1973);C. Becchi:Comm. Math. Phys.,33, 97 (1973).

    Article  ADS  Google Scholar 

  9. G. ’t Hooft andM. Veltman:Nucl. Phys.,44 B, 189 (1972);C. Bollini andJ. Giambiagi:Nuovo Cimento,12 A, 20 (1972);G. M. Cicuta andE. Montaldi:Lett. Nuovo Cimento,4, 329 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  10. T. Marinucci andM. Tonin:Nuovo Cimento,31 A, 381 (1976).

    Article  ADS  Google Scholar 

  11. C. Becchi, A. Rouet andR. Stora:Comm. Math. Phys.,42, 127 (1975);Ann. of Phys.,98, 287 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  12. C. G. Callan:Phys. Rev. D,2, 1541 (1970);K. Symanzik:Comm. Math. Phys.,18, 227 (1970).

    Article  ADS  Google Scholar 

  13. We follow, whenever possible, the same notation as in ref. (13).

    Article  MathSciNet  Google Scholar 

  14. G. Costa andM. Tonin:Riv. Nuovo Cimento,5, 29 (1975).

    Article  MathSciNet  Google Scholar 

  15. C. Bollini andJ. Giambiagi:Acta Phys. Austriaca,38, 211 (1973);D. A. Akyeampong andR. Delbourgo:Nuovo Cimento,17 A, 578 (1973).

    Google Scholar 

  16. P. Breitenlohner andD. Maison: preprint MPI-PAE/PTh 25/74.

  17. W. Bardeen:Phys. Rev.,184, 1848 (1969).

    Article  ADS  Google Scholar 

  18. J. Wess andB. Zumino:Phys. Lett.,37 B, 95 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  19. First reference quoted in (9) andD. M. Capper andG. Leibbrandt:Journ. Math. Phys.,15, 795 (1974).

  20. J. Julve andM. Tonin:Nuovo Cimento,29 A, 85 (1975).

    Article  ADS  Google Scholar 

  21. J. A. Dixon andJ. C. Taylor:Nucl. Phys.,78 B, 552 (1974);J. Zinn-Justin: Lectures atInternational Summer Institute for Theoretical Physics (Bonn, 1974);S. D. Joglekar andB. W. Lee: preprint Fermilab Pub. 75/50 THY (1975);W. S. Deans andJ. A. Dixon: Oxford preprint (1975).

    Article  ADS  Google Scholar 

  22. G. Immirzi: to be published.

  23. J. A. Dixon:Nucl. Phys.,99 B, 420 (1975).

    Article  ADS  Google Scholar 

  24. H. Kluberg-Stern andJ. B. Zuber:Phys. Rev. D,12, 3159 (1975).

    Article  ADS  Google Scholar 

  25. G. ’t Hooft:Nucl. Phys.,61 B, 455 (1973).

    Article  MathSciNet  ADS  Google Scholar 

  26. J. C. Collins andA. J. Macfarlane:Phys. Rev. D,10, 1201 (1974).

    Article  ADS  Google Scholar 

  27. B. S. De Witt:Phys. Rev.,162, 1195, 1239 (1967);J. Honerkamp:Nucl. Phys.,48 B, 269 (1972).

    Article  ADS  Google Scholar 

  28. G. ’t Hooft:Nucl. Phys.,62 B, 444 (1973).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Fisica dell’Università, Padova, Italia

    G. Costa, T. Marinucci & M. Tonin

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Italia

    G. Costa, T. Marinucci & M. Tonin

  3. Instituto de Estructura de la Materia, CSIC, Madrid, España

    J. Julve

Authors
  1. G. Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Marinucci
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Tonin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Julve
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Costa, G., Marinucci, T., Tonin, M. et al. Non-abelian gauge theories and triangle anomalies. Nuov Cim A 38, 373–412 (1977). https://doi.org/10.1007/BF02730012

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02730012

Search

Navigation