Skip to main content
SpringerLink
Log in

On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds

  • Published:
Physics of Particles and Nuclei Aims and scope Submit manuscript

Abstract

We review the details of unconstrained Lagrangian formulations for Bose particles propagated on an arbitrary dimensional flat space-time and described by the unitary irreducible integer higher-spin representations of the Poincare group subject to Young tableaux Y(s 1, ..., s k ) with k rows. The procedure is based on the construction of scalar auxiliary oscillator realizations for the symplectic sp(2k) algebra which encodes the second-class operator constraints subsystem in the HS symmetry algebra. Application of an universal BRST approach reproduces gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive bosonic fields of any spin with appropriate number of auxiliary fields.

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

Access this article

Log in via an institution

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. D. Feldman, P. F. Perez, and P. Nath, “R-Parity Conservation via the Stueckelberg Mechanism: LHC and Dark Matter Signals,” J. High Energy Phys. 1201, 038 (2012).

    Article  ADS  Google Scholar 

  2. M. Vasiliev, “Higher Spin Gauge Theories in Various Dimensions,” Fortsch. Phys. 52, 707–717 (2004); D. Sorokin, “Introduction to the Classical Theory of Higher Spins,” AIP Conf. Proc. 767, 172–202 (2005); N. Bouatta, G. Compère, and A. Sagnotti, “An Introduction to Free Higher-Spin Fields,” Preprint. arXiv:hep-th/0409068; A. Fotopoulos and M. Tsulaia, “Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of BRST Formulation,” Int. J. Mod. Phys. A 24, 1–60 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  3. E. S. Fradkin and G. A. Vilkovisky, “Quantization of Relativistic Systems with Constraints,” Phys. Lett. B 55, 224–226 (1975); I. A. Batalin and E. S. Fradkin, “Operator Quantization of Dynamical Systems with First Class Constraints,” Phys. Lett. B 128, 303 (1983).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. I. L. Buchbinder and A. A. Reshetnyak, “General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic Fields”, Nucl. Phys. B 862, 270–326 (2012). Preprint. arXiv:1110.5044[hep-th]

    Article  ADS  MATH  Google Scholar 

  5. J. M. F. Labastida, “Massless Particles in Arbitrary Representations of the Lorentz Group,” Nucl. Phys. B 322, 185–209 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  6. R. R. Metsaev, “Massless Mixed Symmetry Bosonic Free Fields in d-Dimensional Anti-De Sitter Space-Time,” Phys. Lett. B 354, 78–84 (1995).

    Article  MathSciNet  ADS  Google Scholar 

  7. C. Fronsdal, “Massless Fields with Integer Spin,” Phys. Rev. D: Part. Fields 18, 3624–3629 (1978).

    Article  ADS  Google Scholar 

  8. C. Fronsdal, “Singletons and Massless, Integer-Spin Fields on De Sitter Space,” Phys. Rev. D: Part. Fields 20, 848–856 (1979); M. A. Vasiliev, “Gauge Form of Description of Massless Fields with Arbitrary Spin,” Yad. Fiz. 32, 855–861 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  9. V. E. Lopatin and M. A. Vasiliev, “Free Massless Bosonic Fields of Arbitrary Spin in d-Dimensional De Sitter Space,” Mod. Phys. Lett. A 3, 257–265 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  10. L. P. S. Singh and C. R. Hagen, “Lagrangian Formulation for Arbitrary Spin. 1. The Bosonic Case,” Phys. Rev. D: Part. Fields 9, 898–909 (1974).

    Article  ADS  Google Scholar 

  11. Yu. M. Zinoviev, “On Massive High Spin Particles in AdS,” Preprint. arXiv:hep-th/0108192; R. R. Mestaev, “Massive Totally Symmetric Fields in AdS(d) Phys. Lett. B 590, 95–104 (2004)

    Google Scholar 

  12. C. Burdik, A. Pashnev, and M. Tsulaia, “Auxiliary Representations of Lie Algebras and the BRST Constructions,” Mod. Phys. Lett. A 15, 281–291 (2000).

    Article  MathSciNet  ADS  Google Scholar 

  13. C. Burdik, A. Pashnev, and M. Tsulaia, “On the Mixed Symmetry Irreducible Representations of Poincare Group in the BRST Approach,” Mod. Phys. Lett. A 16, 731–746 (2001).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. I. Buchbinder, V. Krykhtin, and H. Takata, “Gauge Invariant Lagrangian Construction for Massive Bosonic Mixed-Symmetry Higher Spin Fields,” Phys. Lett. B 656, 253 (2007).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. I. L. Buchbinder, V. A. Krykhtin, and A. A. Reshetnyak, “BRST Approach to Lagrangian Construction for Fermionic HS Fields in AdS Space,” Nucl. Phys. B 787, 211–240 (2007).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. E. D. Skvortsov, “Frame-Like Actions for Massless Mixed-Symmetry Fields in Minkowski Space,” Nucl. Phys. B 808, 569 (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. A. Campoleoni, D. Francia, J. Mourad, and A. Sagnotti, “Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields,” Nucl.Phys. B 815, 289–357 (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Non-Linear Media Physics, Institute of Strength Physics and Materials Science, Tomsk, 634021, Russia

    A. A. Reshetnyak

Authors
  1. A. A. Reshetnyak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Reshetnyak.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reshetnyak, A.A. On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds. Phys. Part. Nuclei 43, 689–693 (2012). https://doi.org/10.1134/S1063779612050322

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063779612050322

Keywords

Search

Navigation