Abstract
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.
Article PDF
Similar content being viewed by others
References
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].
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].
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].
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].
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].
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].
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].
M. Vasiliev, Higher spin theories and Sp(2M) invariant space-time, hep-th/0301235 [INSPIRE].
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].
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].
R. Schrader, The Maxwell group and the quantum theory of particles in classical homogeneous electromagnetic fields, Fortsch. Phys. 20 (1972) 701 [INSPIRE].
J. Beckers and V. Hussin, Minimal electromagnetic coupling schemes. II. Relativistic and nonrelativistic Maxwell groups, J. Math. Phys. 24 (1983) 1295 [INSPIRE].
D.V. Soroka and V.A. Soroka, Tensor extension of the Poincaré algebra, Phys. Lett. B 607 (2005) 302 [hep-th/0410012] [INSPIRE].
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].
S. Bonanos and J. Gomis, Infinite sequence of Poincaré group extensions: structure and dynamics, J. Phys. A 43 (2010) 015201 [arXiv:0812.4140] [INSPIRE].
J. Gomis, K. Kamimura and J. Lukierski, Deformations of Maxwell algebra and their dynamical realizations, JHEP 08 (2009) 039 [arXiv:0906.4464] [INSPIRE].
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].
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].
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].
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].
T. Shirafuji, Lagrangian mechanics of massless particles with spin, Prog. Theor. Phys. 70 (1983) 18 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, Cubic interaction in extended theories of massless higher spin fields, Nucl. Phys. B 291 (1987) 141 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].
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].
T. Curtright, Are there any superstrings in eleven-dimensions?, Phys. Rev. Lett. 60 (1988) 393 [Erratum ibid. 60 (1988) 1990] [INSPIRE].
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].
E. Sezgin, The M algebra, Phys. Lett. B 392 (1997) 323 [hep-th/9609086] [INSPIRE].
S. Fedoruk and V. Zima, Massive superparticle with tensorial central charges, Mod. Phys. Lett. A 15 (2000) 2281 [hep-th/0009166] [INSPIRE].
S. Fedoruk and E. Ivanov, Master higher-spin particle, Class. Quant. Grav. 23 (2006) 5195 [hep-th/0604111] [INSPIRE].
D.V. Soroka and V.A. Soroka, Another approach to cosmological term problem, talk at the International Workshop Supersymmetries and Quantum Symmetries (SQS’2011 ), July 18-23, Dubna, Russia (2011).
M. Porrati, R. Rahman and A. Sagnotti, String theory and the Velo-Zwanziger problem, Nucl. Phys. B 846 (2011) 250 [arXiv:1011.6411] [INSPIRE].
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].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1210.1506
On leave of absence from V.N. Karazin Kharkov National University, Ukraine. (Sergey Fedoruk)
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Fedoruk, S., Lukierski, J. New spinorial particle model in tensorial space-time and interacting higher spin fields. J. High Energ. Phys. 2013, 128 (2013). https://doi.org/10.1007/JHEP02(2013)128
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2013)128