Skip to main content
SpringerLink
Log in

Weyl and Majorana Spinors as Pure Goldstone Bosons

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

General spinors in polar form display a structure that is made up by real scalar degrees of freedom plus six components which can be recognized as Goldstone bosons: in the present paper we show that of all singular spinors, Weyl and Majorana spinors have no real degree of freedom and so that they can be interpreted as pure Goldstone states.

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

Data Availability Statement

Manuscript has associated data in a repository.

References

  1. Abłamowicz, R., Gonçalves, I., da Rocha, R.: Bilinear covariants and spinor fields duality in quantum Clifford algebras. J. Math. Phys. 55, 103501 (2014)

    Article  MathSciNet  ADS  Google Scholar 

  2. Ahluwalia, D.V., Grumiller, D.: Spin half fermions with mass dimension one: theory, phenomenology, and dark matter. JCAP 0507, 012 (2005)

    Article  ADS  Google Scholar 

  3. Ahluwalia, D.V., Grumiller, D.: Dark matter: a spin one half fermion field with mass dimension one? Phys. Rev. D 72, 067701 (2005)

    Article  ADS  Google Scholar 

  4. Ahluwalia, D.V.: Evading Weinberg’s no-go theorem to construct mass dimension one fermions: constructing darkness. EPL 118, 60001 (2017)

    Article  Google Scholar 

  5. Ahluwalia, D.V.: The theory of local mass dimension one fermions of spin one half. Adv. Appl. Clifford Algebras 27, 2247 (2017)

    Article  MathSciNet  Google Scholar 

  6. Cavalcanti, R.T.: Classification of singular spinor fields and other mass dimension one fermions. Int. J. Mod. Phys. D 23, 1444002 (2014)

    Article  ADS  Google Scholar 

  7. da Rocha, R., Fabbri, L., Hoff da Silva, J.M., Cavalcanti, R.T., Silva-Neto, J.A.: Flag-dipole spinor fields in ESK gravities. J. Math. Phys. 54, 102505 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  8. da Rocha, R., Hoff da Silva, J.M.: From Dirac spinor fields to ELKO. J. Math. Phys. 48, 123517 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  9. da Rocha, R., Hoff da Silva, J.M.: ELKO, flagpole and flag-dipole spinor fields, and the instanton Hopf fibration. Adv. Appl. Clifford Algebras 20, 847 (2010)

    Article  MathSciNet  Google Scholar 

  10. Fabbri, L.: The most general cosmological dynamics for ELKO matter fields. Phys. Lett. B 704, 255 (2011)

    Article  ADS  Google Scholar 

  11. Fabbri, L.: A generally-relativistic gauge classification of the Dirac fields. Int. J. Geom. Meth. Mod. Phys. 13, 1650078 (2016)

    Article  MathSciNet  Google Scholar 

  12. Fabbri, L.: Covariant inertial forces for spinors. Eur. Phys. J. C 78, 783 (2018)

    Article  ADS  Google Scholar 

  13. Fabbri, L.: Torsion gravity for Dirac fields. Int. J. Geom. Meth. Mod. Phys. 14, 1750037 (2017)

    Article  MathSciNet  Google Scholar 

  14. Fabbri, L.: Polar solutions with tensorial connection of the spinor equation. Eur. Phys. J. C 79, 188 (2019)

    Article  ADS  Google Scholar 

  15. Fabbri, L.: Spinors in polar form. Eur. Phys. J. Plus 136, 354 (2021)

    Article  Google Scholar 

  16. Fabbri, L., Rogerio, R.J.B.: Polar form of spinor fields from regular to singular: the flag-dipoles. Eur. Phys. J. C 80, 880 (2020)

    Article  ADS  Google Scholar 

  17. Fabbri, L.: Spinor fields, singular structures, charge conjugation, ELKO and neutrino masses. Adv. Appl. Clifford Algebras 28, 7 (2018)

    Article  MathSciNet  Google Scholar 

  18. Fabbri, L.: ELKO in polar form. Eur. Phys. J. ST 229, 2117 (2020)

    Article  Google Scholar 

  19. Hoff da Silva, J.M., Cavalcanti, R.T.: Revealing how different spinors can be: the Lounesto spinor classification. Mod. Phys. Lett. A 32, 1730032 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  20. Hoff da Silva, J.M., da Rocha, R.: From Dirac action to ELKO action. Int. J. Mod. Phys. A 24, 3227 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  21. Hoff da Silva, J.M., da Rocha, R.: Unfolding physics from the algebraic classification of spinor fields. Phys. Lett. B 718, 1519 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  22. Lounesto, P.: Clifford Algebras and Spinors. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  23. Rodrigues, W.A., da Rocha, R., Vaz, J.: Hidden consequence of active local Lorentz invariance. Int. J. Geom. Meth. Mod. Phys. 2, 305 (2005)

    Article  MathSciNet  Google Scholar 

  24. Vignolo, S., Fabbri, L., Cianci, R.: Dirac spinors in Bianchi-I f(R)-cosmology with torsion. J. Math. Phys. 52, 112502 (2011)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DIME, Sez. Metodi e Modelli Matematici, Università di Genova, Via all’Opera Pia 15, 16145, Genoa, Italy

    Luca Fabbri

Authors
  1. Luca Fabbri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luca Fabbri.

Ethics declarations

Conflict of interest

There is no conflict of interest.

Additional information

Communicated by Roldão da Rocha.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fabbri, L. Weyl and Majorana Spinors as Pure Goldstone Bosons. Adv. Appl. Clifford Algebras 32, 3 (2022). https://doi.org/10.1007/s00006-021-01188-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00006-021-01188-7

Keywords

Mathematics Subject Classification

Search

Navigation