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Continuous-spin field propagator and interaction with matter

A preprint version of the article is available at arXiv.

Abstract

Action principles for the single and double valued continuous-spin representations of the Poincaré group have been recently proposed in a Segal-like formulation. We address three related issues: first, we explain how to obtain these actions directly from the Fronsdal-like and Fang-Fronsdal-like equations by solving the traceless constraints in Fourier space. Second, we introduce a current, similar to the one of Berends, Burgers and Van Dam, which is bilinear in a pair of scalar matter fields, to which the bosonic continuous-spin field can couple minimally. Third, we investigate the current exchange mediated by a continuous-spin particle obtained from this action principle and investigate whether it propagates the right degrees of freedom, and whether it reproduces the known result for massless higher-spin fields in the helicity limit.

References

  1. E.P. Wigner, On Unitary Representations of the Inhomogeneous Lorentz Group, Annals Math. 40 (1939) 149 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  2. X. Bekaert and N. Boulanger, The Unitary representations of the Poincaré group in any spacetime dimension, hep-th/0611263 [INSPIRE].

  3. E.P. Wigner, Invariant quantum mechanical equations of motion, in International Atomic Energy Agency, Vienna (1963) [INSPIRE].

  4. X. Bekaert and E.D. Skvortsov, Elementary particles with continuous spin, Int. J. Mod. Phys. A 32 (2017) 1730019 [arXiv:1708.01030] [INSPIRE].

  5. A.M. Khan and P. Ramond, Continuous spin representations from group contraction, J. Math. Phys. 46 (2005) 053515 [Erratum ibid. 46 (2005) 079901] [hep-th/0410107] [INSPIRE].

  6. C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18 (1978) 3624 [INSPIRE].

  7. J. Fang and C. Fronsdal, Massless Fields with Half Integral Spin, Phys. Rev. D 18 (1978) 3630 [INSPIRE].

  8. X. Bekaert and J. Mourad, The continuous spin limit of higher spin field equations, JHEP 01 (2006) 115 [hep-th/0509092] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  9. P. Schuster and N. Toro, Continuous-spin particle field theory with helicity correspondence, Phys. Rev. D 91 (2015) 025023 [arXiv:1404.0675] [INSPIRE].

  10. V.O. Rivelles, Gauge Theory Formulations for Continuous and Higher Spin Fields, Phys. Rev. D 91 (2015) 125035 [arXiv:1408.3576] [INSPIRE].

  11. V.O. Rivelles, Remarks on a Gauge Theory for Continuous Spin Particles, Eur. Phys. J. C 77 (2017) 433 [arXiv:1607.01316] [INSPIRE].

  12. A.Yu. Segal, A Generating formulation for free higher spin massless fields, hep-th/0103028 [INSPIRE].

  13. X. Bekaert, M. Najafizadeh and M.R. Setare, A gauge field theory of fermionic Continuous-Spin Particles, Phys. Lett. B 760 (2016) 320 [arXiv:1506.00973] [INSPIRE].

  14. R.R. Metsaev, Continuous spin gauge field in (A)dS space, Phys. Lett. B 767 (2017) 458 [arXiv:1610.00657] [INSPIRE].

  15. R.R. Metsaev, Fermionic continuous spin gauge field in (A)dS space, Phys. Lett. B 773 (2017) 135 [arXiv:1703.05780] [INSPIRE].

  16. Yu.M. Zinoviev, Infinite spin fields in D = 3 and beyond, Universe 3 (2017) 63 [arXiv:1707.08832] [INSPIRE].

  17. M. Najafizadeh, Modified Wigner equations and continuous spin gauge field, arXiv:1708.00827 [INSPIRE].

  18. E.P. Wigner, Relativistische Wellengleichungen, Z. Phys. 124 (1947) 665.

    ADS  MathSciNet  Article  MATH  Google Scholar 

  19. V. Bargmann and E.P. Wigner, Group Theoretical Discussion of Relativistic Wave Equations, Proc. Nat. Acad. Sci. 34 (1948) 211 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  20. X. Bekaert, E. Joung and J. Mourad, On higher spin interactions with matter, JHEP 05 (2009) 126 [arXiv:0903.3338] [INSPIRE].

    ADS  Article  Google Scholar 

  21. F.A. Berends, G.J.H. Burgers and H. van Dam, Explicit Construction of Conserved Currents for Massless Fields of Arbitrary Spin, Nucl. Phys. B 271 (1986) 429 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  22. A. Fotopoulos and M. Tsulaia, On the Tensionless Limit of String theory, Off-Shell Higher Spin Interaction Vertices and BCFW Recursion Relations, JHEP 11 (2010) 086 [arXiv:1009.0727] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  23. M. Taronna, Higher-Spin Interactions: four-point functions and beyond, JHEP 04 (2012) 029 [arXiv:1107.5843] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  24. D. Ponomarev and A.A. Tseytlin, On quantum corrections in higher-spin theory in flat space, JHEP 05 (2016) 184 [arXiv:1603.06273] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  25. C. Sleight and M. Taronna, Higher-Spin Algebras, Holography and Flat Space, JHEP 02 (2017) 095 [arXiv:1609.00991] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  26. D. Francia, J. Mourad and A. Sagnotti, Current Exchanges and Unconstrained Higher Spins, Nucl. Phys. B 773 (2007) 203 [hep-th/0701163] [INSPIRE].

  27. K.-H. Rehren, Pauli-Lubanski limit and stress-energy tensor for infinite-spin fields, arXiv:1709.04858 [INSPIRE].

  28. R.R. Metsaev, Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields, arXiv:1709.08596 [INSPIRE].

  29. A.Y. Segal, Conformal higher spin theory, Nucl. Phys. B 664 (2003) 59 [hep-th/0207212] [INSPIRE].

  30. M. Abramowitz and I.A. Stegun eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical tables, Dover (1972).

  31. H. Bateman, Tables of Integral Transforms, vol. 2, McGraw-Hill book company (1954).

  32. N.Ja. Vilenkin, Special Functions and the Theory of Group Representations, American Mathematical Society (1968).

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Correspondence to Xavier Bekaert.

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ArXiv ePrint: 1710.05788

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Bekaert, X., Mourad, J. & Najafizadeh, M. Continuous-spin field propagator and interaction with matter. J. High Energ. Phys. 2017, 113 (2017). https://doi.org/10.1007/JHEP11(2017)113

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Keywords

  • Higher Spin Symmetry
  • Space-Time Symmetries
  • Gauge Symmetry