Journal of High Energy Physics

, 2013:128 | Cite as

New spinorial particle model in tensorial space-time and interacting higher spin fields

Open Access


The Maxwell-covariant particle model is formulated in tensorial extended D = 4 space-time (x μ , z μν ) parametrized by ten-dimensional coset of D = 4 Maxwell group, with added auxiliary Weyl spinors λ α , y α . We provide the Hamiltonian quantization of the model and demonstrate that first class constraints modify the known equations obtained for massless higher spin fields in flat tensorial space-time. We obtain the Maxwell-covariant field equations for new infinite dimensional spin multiplets. The component fields assigned to different spin values are linked by couplings proportional to rescaled electromagnetic coupling constant \( \widetilde{e}=e\,m \), where m is the mass-like parameter introduced in our model. We discuss briefly the geometry of our tensorial space-time with constant torsion and its relation with the presence of constant electromagnetic background.


Space-Time Symmetries Field Theories in Higher Dimensions Differential and Algebraic Geometry 


  1. [1]
    I.A. Bandos and J. Lukierski, Tensorial central charges and new superparticle models with fundamental spinor coordinates, Mod. Phys. Lett. A 14 (1999) 1257 [hep-th/9811022] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    I.A. Bandos, J. Lukierski and D.P. Sorokin, Superparticle models with tensorial central charges, Phys. Rev. D 61 (2000) 045002 [hep-th/9904109] [INSPIRE].MathSciNetADSGoogle Scholar
  3. [3]
    I.A. Bandos, J. Lukierski, C. Preitschopf and D.P. Sorokin, OSp supergroup manifolds, superparticles and supertwistors, Phys. Rev. D 61 (2000) 065009 [hep-th/9907113] [INSPIRE].MathSciNetADSGoogle Scholar
  4. [4]
    M. Vasiliev, Conformal higher spin symmetries of 4D massless supermultiplets and OSp(L, 2M) invariant equations in generalized (super)space, Phys. Rev. D 66 (2002) 066006 [hep-th/0106149] [INSPIRE].MathSciNetADSGoogle Scholar
  5. [5]
    M. Plyushchay, D. Sorokin and M. Tsulaia, Higher spins from tensorial charges and OSp(N|2n) symmetry, JHEP 04 (2003) 013 [hep-th/0301067] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    M. Plyushchay, D. Sorokin and M. Tsulaia, GL flatness of OSp(1|2n) and higher spin field theory from dynamics in tensorial spaces, hep-th/0310297 [INSPIRE].
  7. [7]
    I. Bandos, X. Bekaert, J. de Azcarraga, D. Sorokin and M. Tsulaia, Dynamics of higher spin fields and tensorial space, JHEP 05 (2005) 031 [hep-th/0501113] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M. Vasiliev, Higher spin theories and Sp(2M) invariant space-time, hep-th/0301235 [INSPIRE].
  9. [9]
    M. Vasiliev, On conformal, SL(4, \( \mathbb{R} \)) and Sp(8, R) symmetries of 4D massless fields, Nucl. Phys. B 793 (2008) 469 [arXiv:0707.1085] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    H. Bacry, P. Combe and J. Richard, Group-theoretical analysis of elementary particles in an external electromagnetic field. 1. The relativistic particle in a constant and uniform field, Nuovo Cim. A 67 (1970) 267 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    R. Schrader, The Maxwell group and the quantum theory of particles in classical homogeneous electromagnetic fields, Fortsch. Phys. 20 (1972) 701 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    J. Beckers and V. Hussin, Minimal electromagnetic coupling schemes. II. Relativistic and nonrelativistic Maxwell groups, J. Math. Phys. 24 (1983) 1295 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    D.V. Soroka and V.A. Soroka, Tensor extension of the Poincaré algebra, Phys. Lett. B 607 (2005) 302 [hep-th/0410012] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    S. Bonanos and J. Gomis, A note on the Chevalley-Eilenberg cohomology for the Galilei and Poincaré algebras, J. Phys. A 42 (2009) 145206 [arXiv:0808.2243] [INSPIRE].MathSciNetADSGoogle Scholar
  15. [15]
    S. Bonanos and J. Gomis, Infinite sequence of Poincaré group extensions: structure and dynamics, J. Phys. A 43 (2010) 015201 [arXiv:0812.4140] [INSPIRE].MathSciNetADSGoogle Scholar
  16. [16]
    J. Gomis, K. Kamimura and J. Lukierski, Deformations of Maxwell algebra and their dynamical realizations, JHEP 08 (2009) 039 [arXiv:0906.4464] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    J.A. de Azcarraga, K. Kamimura and J. Lukierski, Generalized cosmological term from Maxwell symmetries, Phys. Rev. D 83 (2011) 124036 [arXiv:1012.4402] [INSPIRE].ADSGoogle Scholar
  18. [18]
    D.V. Soroka and V.A. Soroka, Gauge semi-simple extension of the Poincaré group, Phys. Lett. B 707 (2012) 160 [arXiv:1101.1591] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    R. Durka, J. Kowalski-Glikman and M. Szczachor, Gauged AdS-Maxwell algebra and gravity, Mod. Phys. Lett. A 26 (2011) 2689 [arXiv:1107.4728] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    S. Fedoruk and J. Lukierski, New particle model in extended space-time and covariantization of planar Landau dynamics, Phys. Lett. B 718 (2012) 646 [arXiv:1207.5683] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    T. Shirafuji, Lagrangian mechanics of massless particles with spin, Prog. Theor. Phys. 70 (1983) 18 [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  22. [22]
    E.S. Fradkin and M.A. Vasiliev, Cubic interaction in extended theories of massless higher spin fields, Nucl. Phys. B 291 (1987) 141 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    E.S. Fradkin and M.A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    X. Bekaert, N. Boulanger and P. Sundell, How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples, Rev. Mod. Phys. 84 (2012) 987 [arXiv:1007.0435] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    T. Curtright, Are there any superstrings in eleven-dimensions?, Phys. Rev. Lett. 60 (1988) 393 [Erratum ibid. 60 (1988) 1990] [INSPIRE].
  26. [26]
    J. de Azcarraga, J.P. Gauntlett, J. Izquierdo and P. Townsend, Topological extensions of the supersymmetry algebra for extended objects, Phys. Rev. Lett. 63 (1989) 2443 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    E. Sezgin, The M algebra, Phys. Lett. B 392 (1997) 323 [hep-th/9609086] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    S. Fedoruk and V. Zima, Massive superparticle with tensorial central charges, Mod. Phys. Lett. A 15 (2000) 2281 [hep-th/0009166] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  29. [29]
    S. Fedoruk and E. Ivanov, Master higher-spin particle, Class. Quant. Grav. 23 (2006) 5195 [hep-th/0604111] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  30. [30]
    D.V. Soroka and V.A. Soroka, Another approach to cosmological term problem, talk at the International Workshop Supersymmetries and Quantum Symmetries (SQS2011 ), July 18-23, Dubna, Russia (2011).
  31. [31]
    M. Porrati, R. Rahman and A. Sagnotti, String theory and the Velo-Zwanziger problem, Nucl. Phys. B 846 (2011) 250 [arXiv:1011.6411] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    I. Buchbinder, T. Snegirev and Y. Zinoviev, Cubic interaction vertex of higher-spin fields with external electromagnetic field, Nucl. Phys. B 864 (2012) 694 [arXiv:1204.2341] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA 2013

Authors and Affiliations

  1. 1.Bogoliubov Laboratory of Theoretical Physics, JINRDubnaRussia
  2. 2.Institute for Theoretical PhysicsUniversity of WroclawWroclawPoland

Personalised recommendations