Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 061, 17 pages      arXiv:0804.0522      http://dx.doi.org/10.3842/SIGMA.2008.061

Schwinger-Fronsdal Theory of Abelian Tensor Gauge Fields

Sebastian Guttenberg and George Savvidy
Institute of Nuclear Physics, Demokritos National Research Center, Agia Paraskevi, GR-15310 Athens, Greece

Received April 23, 2008, in final form September 01, 2008; Published online September 04, 2008

Abstract
This review is devoted to the Schwinger and Fronsdal theory of Abelian tensor gauge fields. The theory describes the propagation of free massless gauge bosons of integer helicities and their interaction with external currents. Self-consistency of its equations requires only the traceless part of the current divergence to vanish. The essence of the theory is given by the fact that this weaker current conservation is enough to guarantee the unitarity of the theory. Physically this means that only waves with transverse polarizations are propagating very far from the sources. The question whether such currents exist should be answered by a fully interacting theory. We also suggest an equivalent representation of the corresponding action.

Key words: Abelian gauge fields; Abelian tensor gauge fields; high spin fields; conserved currents; weakly conserved currents.

pdf (297 kb)   ps (191 kb)   tex (22 kb)

References

  1. Schwinger J., Particles, sources, and fields, Addison-Wesley, Reading, MA, 1970.
  2. Fronsdal C., Massless fields with integer spin, Phys. Rev. D 18 (1978), 3624-3629.
  3. Singh L.P.S., Hagen C.R., Lagrangian formulation for arbitrary spin. I. The boson case, Phys. Rev. D 9 (1974), 898-909.
  4. Feynman R.P., Feynman lecture on gravitation, Westview Press, 2002.
  5. Fierz M., Über die relativistische Theorie kräftefreier Teilchen mit beliebigem Spin, Helv. Phys. Acta. 12 (1939), 3-27.
  6. Chang S.J., Lagrange formulation for systems with higher spin, Phys. Rev. 161 (1967), 1308-1315.
  7. van Dam H., Veltman M.J.G., Massive and massless Yang-Mills and gravitational fields, Nuclear Phys. B 22 (1970), 397-411.
  8. Curtright T., Massless field supermultiplets with arbitrary spin, Phys. Lett. B 85 (1979), 219-224.
  9. Bengtsson A.K., Bengtsson I., Brink L., Cubic interaction terms for arbitrary spin, Nuclear Phys. B 227 (1983), 31-40.
  10. Bengtsson A.K., Bengtsson I., Brink L., Cubic interaction terms for arbitrarily extended supermultiplets, Nuclear Phys. B 227 (1983), 41-49.
  11. Bengtsson A.K.H., Bengtsson I., Linden N., Interacting higher spin gauge fields on the light front, Classical Quantum Gravity 4 (1987), 1333-1345.
  12. Berends F.A., Burgers G.J.H., van Dam H., On the theoretical problems in constructing interactions involving higher-spin massless particles, Nuclear Phys. B 260 (1985), 295-322.
  13. Berends F.A., Burgers G.J.H., van Dam H., On spin three selfinteractions, Z. Phys. C 24 (1984), 247-254.
  14. de Wit B., Freedman D.Z., Systematics of higher spin gauge fields, Phys. Rev. D (3) 21 (1980), 358-367.
  15. Bengtsson A.K.H., Structure of higher spin gauge interactions, J. Math. Phys. 48 (2007) 072302, 35 pages, hep-th/0611067.
  16. Savvidy G., Non-Abelian tensor gauge fields: enhanced symmetries, hep-th/0604118 (see Section 6).
  17. Bengtsson A.K.H., Towards unifying structures in higher spin gauge symmetry, SIGMA 4 (2008), 013, 23 pages, arXiv:0802.0479.
  18. Bekaert X., Cnockaert S., Iazeolla C., Vasiliev M.A., Nonlinear higher spin theories in various dimensions, hep-th/0503128.
  19. Vasiliev M.A., Higher-spin gauge theories in four, three and two dimensions, Internat. J. Modern Phys. D 5 (1996), 763-797, hep-th/9611024.
  20. Vasiliev M.A., Higher spin gauge theories: star-product and AdS space, hep-th/9910096.
  21. Engquist J., Sezgin E., Sundell P., On N = 1,2,4 higher spin gauge theories in four dimensions, Classical Quantum Gravity 19 (2002), 6175-6196, hep-th/0207101.
  22. Sezgin E., Sundell P., Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, J. High Energy Phys. 2005 (2005), no. 7, 044, 26 pages, hep-th/0305040.
  23. Francia D., Sagnotti A., On the geometry of higher-spin gauge fields, Classical Quantum Gravity 20 (2003), S473-S486, hep-th/0212185.
  24. Francia D., Mourad J., Sagnotti A., Current exchanges and unconstrained higher spins, Nuclear Phys. B 773 (2007), 203-237, hep-th/0701163.
  25. Sorokin D., Introduction to the classical theory of higher spins, AIP Conf. Proc. 767 (2005), 172-202, hep-th/0405069.
  26. Francia D., Sagnotti A., Free geometric equations for higher spins, Phys. Lett. B 543 (2002), 303-310, hep-th/0207002.
  27. Savvidy G., Non-Abelian tensor gauge fields: generalization of Yang-Mills theory, Phys. Lett. B 625 (2005), 341-350, hep-th/0509049.
  28. Savvidy G., Non-Abelian tensor gauge fields. I, Internat. J. Modern Phys. A 21 (2006), 4931-4957.
  29. Savvidy G., Non-Abelian tensor gauge fields. II, Internat. J. Modern Phys. A 21 (2006), 4959-4977.
  30. Barrett J. K., Savvidy G., A dual Lagrangian for non-Abelian tensor gauge fields, Phys. Lett. B 652 (2007), 141-145, arXiv:0704.3164
  31. Weinberg S., Feynman rules for any spin, Phys. Rev. (2) 133 (1964), B1318-B1332.
  32. Weinberg S., The quantum theory of fields, Vol. 1, Foundations, Cambridge University Press, Cambridge, 1995.
  33. Konitopoulos S., Savvidy G., Production of spin-two gauge bosons, arXiv:0804.0847.

Previous article   Next article   Contents of Volume 4 (2008)