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A possibility to describe models of massive non-Abelian gauge fields in the framework of a renormalizable theory

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Abstract

We propose a renormalizable theory of massive non-Abelian gauge fields that does not require the existence of observable scalar fields.

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References

  1. F. Englert and R. Brout, “Broken symmetry and the mass of gauge vector mesons,” Phys. Lett., 13, 321–323 (1964).

    Article  MathSciNet  Google Scholar 

  2. P. W. Higgs, “Broken symmetries, massless particles, and gauge fields,” Phys. Lett., 12, 132–133 (1964).

    Article  ADS  Google Scholar 

  3. S. Weinberg, “A model of leptons,” Phys. Rev. Lett., 19, 1264–1265 (1967).

    Article  ADS  Google Scholar 

  4. A. Salam, “Weak and electromagnetic interactions,” in: Elementary Particle Physics: Relativistic Groups and Analyticity (Proc. 8th Nobel Symp., Aspenäsgarden, Lerum, Sweden, 19–25 July 1968, N. Svartholm, ed.), Almqvist and Wiksell, Stockholm (1968), pp. 367–377.

    Google Scholar 

  5. S. L. Glashow, “Partial-symmetries of weak interactions,” Nucl. Phys., 22, 579–588 (1961).

    Article  Google Scholar 

  6. A. A. Slavnov, “A Lorentz invariant formulation of the Yang–Mills theory with gauge invariant ghost field Lagrangian,” JHEP, 0808, 047 (2008); arXiv:0807.1795v1 [hep-th] (2008).

    Article  ADS  MathSciNet  Google Scholar 

  7. A. A. Slavnov, “Lorentz-invariant quantization of the Yang–Mills theory free of the Gribov ambiguity,” Theor. Math. Phys., 161, 1497–1502 (2009).

    Article  MATH  Google Scholar 

  8. A. A. Slavnov, “Lorentz-invariant quantization of the Yang–Mills theory without Gribov ambiguity,” Proc. Steklov Inst. Math., 272, 235–245 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Quadri and A. A. Slavnov, “Renormalization of the Yang–Mills theory in the ambiguity-free gauge,” JHEP, 1007, 087 (2010); arXiv:1002.2490v2 [hep-th] (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. A. Quadri and A. A. Slavnov, “Ambiguity-free formulation of the Higgs–Kibble model,” Theor. Math. Phys., 166, 291–302 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. A. Slavnov, “New approach to the quantization of the Yang–Mills field,” Theor. Math. Phys., 183, 585–596 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  12. A. A. Slavnov, “Nonperturbative quantization of models of massive non-Abelian gauge fields with spontaneously broken symmetry,” Theor. Math. Phys., 189, 1645–1650 (2016).

    Article  MATH  Google Scholar 

  13. V. N. Gribov, “Quantization of non-Abelian gauge theories,” Nucl. Phys. B, 139, 1–19 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  14. C. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw-Hill, New York, (1980).

    MATH  Google Scholar 

  15. L. D. Faddeev, “On the separation of self-action and scattering effects in perturbation theory,” Dokl. Akad. Nauk SSSR, 152, 573–576 (1963).

    MathSciNet  Google Scholar 

  16. A. A. Slavnov and L. D. Faddeev, Introduction to the Quantum Theory of Gauge Fields [in Russian], Nauka, Moscow (1988); English transl.: L. D. Faddeev and A. A. Slavnov Gauge Fields: Introduction to Quantum Theory (Frontiers Phys., Vol. 83), Addison-Wesley, Redwood City, Calif. (1991).

    MATH  Google Scholar 

  17. J. M. Cornwall, D. N. Levin, and G. Tiktopoulos, “Derivation of gauge invariance from high-energy unitarity bounds on the S matrix,” Phys. Rev. D, 10, 1145–1167 (1963).

    Article  ADS  Google Scholar 

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Correspondence to A. A. Slavnov.

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This research was supported by a grant from the Russian Science Foundation (Project No. 14-50-00005).

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 193, No. 3, pp. 484–492, December, 2017.

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Slavnov, A.A. A possibility to describe models of massive non-Abelian gauge fields in the framework of a renormalizable theory. Theor Math Phys 193, 1826–1833 (2017). https://doi.org/10.1134/S004057791712008X

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  • DOI: https://doi.org/10.1134/S004057791712008X

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