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Mass shell behaviour of quantum chromodynamics in the axial gauge

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Il Nuovo Cimento A (1965-1970)

Summary

It is shown that, in the noncovariant axial gauge, quark and gluon mass shell renormalization constants (if suitably defined) obey the classic Ward identity of quantum electrodynamicsZ 1=Z 2. Similar relations hold for the pure gluon sector. The validity of such identities in covariant gauges has been proven recently in the literature. The derivation in the axial gauge is considerably simpler than in covariant gauges.

Riassunto

Si mostra che nel gauge assiale non covariante le costanti di rinormalizzazione dello strato di massa del gluone e del quark (se definite in maniera adeguata) obbediscono la classica identità di Ward della elettrodinamica quantisticaZ 1=Z 2. Relazioni simili sono valide per il puro settore gluonico. La validità di tali identità nei gauge covarianti è stata provata recentemente nella letteratura. La derivazione nel gauge assiale è considerevolmente più semplice che nei gauge covarianti.

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References

  1. G. t’Hooft:Nucl. Phys.,33 B, 173 (1971);35 B, 167 (1971); for a review, cf.G. Costa andM. Tonin:Riv. Nuovo Cimento,5, 29 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  2. York Peng Yao:Phys. Rev. Lett.,36, 653 (1976);Th. Appelquist, J. Carazzone, H. Kluberg-Stern andM. Roth:Phys. Rev. Lett.,36, 768 (1976);L. Tyburski:Phys. Rev. Lett.,37, 319 (1976);Nucl. Phys.,116 B, 291 (1976);J. Frenkel, R. Meuldermans, I. Mohammad andJ. C. Taylor:Phys. Lett.,64 B, 211 (1976);Nucl. Phys.,121 B, 58 (1977);A. Garcia Alvarez:Nucl. Phys.,120 B, 355 (1977);T. Kinoshita andA. Ukawa:Phys. Rev. D,13, 1573 (1976);15, 1596 (1977);G. Sterman:Phys. Rev. D,14, 2123 (1976).

    Article  ADS  Google Scholar 

  3. F. Bloch andA. Nordsieck:Phys. Rev.,52, 54 (1937);J. M. Jauch andF. Rohrlich:The Theory of Photons and Electrons (Reading, Mass., 1955).

    Article  ADS  Google Scholar 

  4. The forward direction is more complicated than in QED:C. T. Sachrajda:Phys. Rev. D,14, 1072 (1976);L. Matsson andR. Meuldermans:Phys. Lett.,70 B, 309 (1977).

    Article  ADS  Google Scholar 

  5. P. Cvitanović:Nucl. Phys.,130 B, 114 (1977).

    Article  ADS  Google Scholar 

  6. G. ’t Hooft andM. Veltman:Nucl. Phys.,44 B, 189 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  7. G. Leibbrandt:Rev. Mod. Phys.,47, 849 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  8. L. D. Faddeev andV. N. Popov:Phys. Lett.,25 B, 29 (1967).

    Article  ADS  Google Scholar 

  9. A. Slavnov:Theor. Math. Phys.,10, 99 (1972);J. C. Taylor:Nucl. Phys.,33 B, 436 (1971).

    Article  MathSciNet  Google Scholar 

  10. W. Kummer:Acta Phys. Austr.,41, 315 (1975).

    MathSciNet  Google Scholar 

  11. J. Frenkel:Phys. Rev. D,13, 2325 (1976).

    Article  ADS  Google Scholar 

  12. W. Konetschny andW. Kummer:Nucl. Phys.,100 B, 106 (1975);108 B, 397 (1976).

    Article  ADS  Google Scholar 

  13. A. Sugamoto, H. Yamamoto andN. Nakagawa: University of Tokyo preprint UT-291 (August 1977).

  14. R. L. Arnowitt andS. I. Fickler:Phys. Rev.,127, 1821 (1962);W. Kummer:Acta Phys. Austr.,14, 149 (1961);J. Schwinger:Phys. Rev.,130, 402 (1963);Y. P. Yao:Journ. Math. Phys.,5, 1319 (1964);E. S. Fradkin andI. V. Tyutin:Phys. Rev. D,2, 2841 (1970);A. Chakrabarti andC. Darzens:Phys. Rev. D,9, 2484 (1974);E. Tomboulis:Phys. Rev. D,8, 2736 (1973);R. Delbourgo, A. Salam andJ. Strathdee:Nuovo Cimento,23 A, 237 (1974);J. M. Cornwall:Phys. Rev. D,10, 500 (1974);R. J. Crewther:Weak and Electromagnetic Interactions at High Energies, edited byM. Lévy et al. (New York, N. Y., 1976), p. 345.

    Article  MathSciNet  ADS  Google Scholar 

  15. B. W. Lee:Phys. Lett.,46 B, 214 (1973).

    Article  ADS  Google Scholar 

  16. SeeJ. D. Bjorken andS. D. Drell:Relativistic Quantum Fields (New York, N. Y., 1965).

  17. W. Konetschny andW. Kummer:Nucl. Phys.,124 B, 145 (1977).

    Article  ADS  Google Scholar 

  18. H. Pagels:Phys. Rev. D,15, 2991 (1977).

    Article  ADS  Google Scholar 

  19. J. Frenkel:Phys. Lett.,65 B, 383 (1976);K. J. Kim: Mainz preprint MZ-TH 76/6 (August 1976).

    Article  ADS  Google Scholar 

  20. B. W. Lee andJ. Zinn-Justin:Phys. Rev. D,5, 3121 (1972).

    Article  ADS  Google Scholar 

  21. S. Weinberg:Phys. Rev.,135, B 1049 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  22. J. Frenkel:Phys. Lett.,60 B, 74 (1975).

    Article  ADS  Google Scholar 

  23. J. Frenkel andR. Meuldermans:Phys. Lett.,65 B, 64 (1976).

    Article  ADS  Google Scholar 

  24. I. S. Gradshteyn andI. M. Ryzhik:Table of Integrals, Series and Products (New York, N. Y., 1965).

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Authors and Affiliations

  1. Institut für Theoretische Physik II, Technische Universität Wien, Wien, Austria

    W. Konetschny

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  1. W. Konetschny
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Konetschny, W. Mass shell behaviour of quantum chromodynamics in the axial gauge. Nuov Cim A 44, 465–480 (1978). https://doi.org/10.1007/BF02896335

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  • DOI: https://doi.org/10.1007/BF02896335

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