Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Non-Abelian tensor gauge fields

  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

A recently proposed extension of Yang-Mills theory contains non-Abelian tensor gauge fields. The Lagrangian has quadratic kinetic terms, as well as cubic and quartic terms describing nonlinear interaction of tensor gauge fields with the dimensionless coupling constant. We analyze the particle content of non-Abelian tensor gauge fields. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity 2 and 0. We introduce interaction of the non-Abelian tensor gauge field with fermions and demonstrate that the free equation of motion for the spinor-vector field correctly describes the propagation of massless modes of helicity 3/2. We have found a new metric-independent gauge invariant density which is a four-dimensional analog of the Chern-Simons density. The Lagrangian augmented by this Chern-Simons-like invariant describes the massive Yang-Mills boson, providing a gauge invariant mass gap for a four-dimensional gauge field theory.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. C. N. Yang and R. L. Mills, “Conservation of Isotopic Spin and Isotopic Gauge Invariance,” Phys. Rev. 96, 191–195 (1954).

    Article  MathSciNet  Google Scholar 

  2. S. S. Chern, Topics in Differential Geometry, Ch. III: Theory of Connections (Inst. Adv. Study, Princeton, NJ, 1951).

    Google Scholar 

  3. G. Savvidy, “Non-Abelian Tensor Gauge Fields: Generalization of Yang-Mills Theory,” Phys. Lett. B 625, 341–350 (2005).

    Article  MathSciNet  Google Scholar 

  4. G. Savvidy, “Non-Abelian Tensor Gauge Fields. I,” Int. J. Mod. Phys. A 21, 4931–4957 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Savvidy, “Non-Abelian Tensor Gauge Fields. II,” Int. J. Mod. Phys. A 21, 4959–4977 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  6. S. Coleman and J. Mandula, “All Possible Symmetries of the S Matrix,” Phys. Rev. 159, 1251–1256 (1967).

    Article  MATH  Google Scholar 

  7. R. Haag, J. T. Łopuszański, and M. Sohnius, “All Possible Generators of Supersymmetries of the S-Matrix,” Nucl. Phys. B 88, 257–274 (1975).

    Article  Google Scholar 

  8. J. K. Barrett and G. Savvidy, “A Dual Lagrangian for Non-Abelian Tensor Gauge Fields,” Phys. Lett. B 652, 141–145 (2007).

    Article  MathSciNet  Google Scholar 

  9. G. Savvidy, “Interaction of Non-Abelian Tensor Gauge Fields,” Arm. J. Math. 1, 1–17 (2008); arXiv: 0804.2003 [hep-th].

    MathSciNet  Google Scholar 

  10. W. Rarita and J. Schwinger, “On a Theory of Particles with Half-Integral Spin,” Phys. Rev. 60, 61 (1941).

    Article  MATH  Google Scholar 

  11. L. P. S. Singh and C. R. Hagen, “Lagrangian Formulation for Arbitrary Spin. II: The Fermion Case,” Phys. Rev. D 9, 910–920 (1974).

    Article  Google Scholar 

  12. J. Fang and C. Fronsdal, “Massless Fields with Half-Integral Spin,” Phys. Rev. D 18, 3630–3633 (1978).

    Article  Google Scholar 

  13. G. Savvidy, “Solution of Free Field Equations in Non-Abelian Tensor Gauge Field Theory,” Phys. Lett. B 682, 143–149 (2009).

    Article  MathSciNet  Google Scholar 

  14. J. M. Cornwall, D. N. Levin, and G. Tiktopoulos, “Uniqueness of Spontaneously Broken Gauge Theories,” Phys. Rev. Lett. 30, 1268–1270 (1973); Erratum: Phys. Rev. Lett. 31, 572 (1973).

    Article  Google Scholar 

  15. C. H. Llewellyn Smith, “High-Energy Behaviour and Gauge Symmetry,” Phys. Lett. B 46, 233–236 (1973).

    Article  Google Scholar 

  16. J. Schwinger, “Gauge Invariance and Mass,” Phys. Rev. 125, 397–398 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Schwinger, “Gauge Invariance and Mass. II,” Phys. Rev. 128, 2425–2429 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  18. T. Kunimasa and T. Gotō, “Generalization of the Stueckelberg Formalism to the Massive Yang-Mills Field,” Prog. Theor. Phys. 37, 452–464 (1967).

    Article  Google Scholar 

  19. M. Veltman, “Perturbation Theory of Massive Yang-Mills Fields,” Nucl. Phys. B 7, 637–650 (1968).

    Article  Google Scholar 

  20. A. A. Slavnov and L. D. Faddeev, “Massless and Massive Yang-Mills Fields,” Teor. Mat. Fiz. 3(1), 18–23 (1970) [Theor. Math. Phys. 3, 312–316 (1970)].

    Google Scholar 

  21. H. van Dam and M. Veltman, “Massive and Mass-less Yang-Mills and Gravitational Fields,” Nucl. Phys. B 22, 397–411 (1970).

    Article  Google Scholar 

  22. A. A. Slavnov, “Massive Gauge Fields,” Teor. Mat. Fiz. 10(3), 305–328 (1972) [Theor. Math. Phys. 10, 201–217 (1972)].

    Google Scholar 

  23. M. J. G. Veltman, “Nobel Lecture: FromWeak Interactions to Gravitation,” Rev. Mod. Phys. 72, 341–349 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  24. P. Sikivie, “An Introduction to Technicolor,” Preprint CERN-TH-2951 (1980).

  25. E. Farhi and L. Susskind, “Technicolour,” Phys. Rep. 74, 277–321 (1981).

    Article  Google Scholar 

  26. S. Dimopoulos and J. Ellis, “Challenges for Extended Technicolour Theories,” Nucl. Phys. B 182, 505–528 (1981).

    Article  Google Scholar 

  27. A. A. Slavnov, “Higgs Mechanism as a Collective Effect due to an Extra Dimension,” Teor. Mat. Fiz. 148(3), 339–349 (2006) [Theor. Math. Phys. 148, 1159–1167 (2006)].

    MathSciNet  Google Scholar 

  28. S. Deser, R. Jackiw, and S. Templeton, “Three-Dimensional Massive Gauge Theories,” Phys. Rev. Lett. 48, 975–978 (1982).

    Article  Google Scholar 

  29. S. Deser, R. Jackiw, and S. Templeton, “Topologically Massive Gauge Theories,” Ann. Phys. 140, 372–411 (1982).

    Article  MathSciNet  Google Scholar 

  30. J. F. Schonfeld, “A Mass Term for Three-Dimensional Gauge Fields,” Nucl. Phys. B 185, 157–171 (1981).

    Article  Google Scholar 

  31. E. Cremmer and J. Scherk, “Spontaneous Dynamical Breaking of Gauge Symmetry in Dual Models,” Nucl. Phys. B 72, 117–124 (1974).

    Article  Google Scholar 

  32. C. R. Hagen, “Action-Principle Quantization of the Antisymmetric Tensor Field,” Phys. Rev. D 19, 2367–2369 (1979).

    Article  MathSciNet  Google Scholar 

  33. M. Kalb and P. Ramond, “Classical Direct Interstring Action,” Phys. Rev. D 9, 2273–2284 (1974).

    Article  Google Scholar 

  34. Y. Nambu, “Magnetic and Electric Confinement of Quarks,” Phys. Rep. 23, 250–253 (1976).

    Article  Google Scholar 

  35. V. I. Ogievetskii and I. V. Polubarinov, “The Notoph and Its Possible Interactions,” Yad. Fiz. 4(1), 216–223 (1966) [Sov. J. Nucl. Phys. 4, 156–161 (1967)].

    Google Scholar 

  36. A. Aurilia and Y. Takahashi, “Generalized Maxwell Equations and the Gauge Mixing Mechanism of Mass Generation,” Prog. Theor. Phys. 66, 693–712 (1981).

    Article  Google Scholar 

  37. D. Z. Freedman and P. K. Townsend, “Antisymmetric Tensor Gauge Theories and Non-linear σ-Models,” Nucl. Phys. B 177, 282–296 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  38. A. A. Slavnov and S. A. Frolov, “Quantization of Non-Abelian Antisymmetric Tensor Field,” Teor. Mat. Fiz. 75(2), 201–211 (1988) [Theor. Math. Phys. 75, 470–477 (1988)].

    MathSciNet  Google Scholar 

  39. T. J. Allen, M. J. Bowick, and A. Lahiri, “Topological Mass Generation in (3 + 1)-Dimensions,” Mod. Phys. Lett. A 6, 559–571 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  40. M. Henneaux, V. E. R. Lemes, C. A. G. Sasaki, S. P. Sorella, O. S. Ventura, and L. C. Q. Vilar, “A No-Go Theorem for the Nonabelian Topological Mass Mechanism in Four Dimensions,” Phys. Lett. B 410, 195–202 (1997); arXiv: hep-th/9707129.

    Article  Google Scholar 

  41. A. Lahiri, “Dynamical Non-Abelian Two-Form: BRST Quantization,” Phys. Rev. D 55, 5045–5050 (1997); arXiv: hep-ph/9609510.

    Article  MathSciNet  Google Scholar 

  42. M. Botta Cantcheff, “Doublet Groups, Extended Lie Algebras, and Well Defined Gauge Theories for the Two-Form Field,” Int. J. Mod. Phys. A 20, 2673–2685 (2005); arXiv: hep-th/0310156.

    Article  MathSciNet  MATH  Google Scholar 

  43. G. Savvidy, “Topological Mass Generation in Four-Dimensional Gauge Theory,” arXiv: 1001.2808 [hep-th].

Download references

Author information

Authors and Affiliations

  1. Demokritos National Research Center, Institute of Nuclear Physics, Ag. Paraskevi, GR-15310, Athens, Greece

    George Savvidy

Authors
  1. George Savvidy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George Savvidy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Savvidy, G. Non-Abelian tensor gauge fields. Proc. Steklov Inst. Math. 272, 201–215 (2011). https://doi.org/10.1134/S0081543811010196

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543811010196

Keywords

Search

Navigation