Foundations of Physics

, Volume 39, Issue 1, pp 73–107 | Cite as

A Condensed Matter Interpretation of SM Fermions and Gauge Fields

Article

Abstract

We present the bundle (Aff(3)Λ)(ℝ3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂΛ)(ℝ3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)ℂ)(ℤ3). This space allows a simple physical interpretation as a phase space of a lattice of cells.

We find the SM SU(3)c×SU(2)L×U(1)Y action on (Aff(3)Λ)(ℝ3) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations.

The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ2-valued (spin) field theory.

A metric theory of gravity compatible with this model is presented too.

Keywords

Standard model Ether interpretation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arnowitt, R., Deser, S., Misner, C.W.: The dynamics of general relativity. In: Witten, L. (ed.) Gravitation: An Introduction to Current Research. Wiley, New York (1962) Google Scholar
  2. 2.
    Banks, T., Dothan, Y., Horn, D.: Geometric fermions. Phys. Lett. B 117, 413 (1982) CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Banks, T., Kogut, J., Susskind, L.: PRD 13, 1043 (1996) CrossRefADSGoogle Scholar
  4. 4.
    Becher, P.: Phys. Lett. B 104, 221 (1981) CrossRefADSGoogle Scholar
  5. 5.
    Becher, P., Joos, H.: The Dirac-Kähler equation and fermions on the lattice. Z. Phys. C Part. Fields 15, 343–365 (1982) CrossRefMathSciNetGoogle Scholar
  6. 6.
    Berezin, F.A.: The Method of Second Quantization. Academic Press, New York (1966) MATHGoogle Scholar
  7. 7.
    Bleuer, K.: Helv. Phys. Acta 23(5), 567–586 (1950) Google Scholar
  8. 8.
    Chadha, S., Nielsen, H.B.: Nucl. Phys. B 217, 125–144 (1983) CrossRefADSGoogle Scholar
  9. 9.
    Daviau, C.: Dirac equation in the Clifford algebra of space. In: Dietrich, V., Habetha, K., Jank, G. (eds.) Proc. of Clifford Algebra and Their Applications in Mathematical Physics, Aachen, 1996, pp. 67–87. Kluwer, Dordrecht (1998) Google Scholar
  10. 10.
    Dirac, P.A.M.: Proc. R. Soc. A 114(767), 243–265 (1927) CrossRefADSGoogle Scholar
  11. 11.
    Fermi, E.: Rev. Mod. Phys. 4(1), 87–132 (1932) MATHCrossRefADSGoogle Scholar
  12. 12.
    Frampton, P., Glashow, S.: Chiral color: an alternative to the standard model. Phys. Lett. B 190, 157 (1987) CrossRefADSGoogle Scholar
  13. 13.
    Georgi, H., Glashow, S.: Unity of all elementary-particle forces. Phys. Rev. Lett. 32, 438 (1974) CrossRefADSGoogle Scholar
  14. 14.
    Gupta, S.: Proc. Phys. Lett. B 521, 429 (1950) Google Scholar
  15. 15.
    Gupta, R.: Introduction to lattice QCD. arXiv:hep-lat/9807028 (1998)
  16. 16.
    Hestenes, D.: Space-time structure of weak and electromagnetic interactions. Found. Phys. 12, 153–168 (1982) CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Isham, C.: Canonical quantum gravity and the problem of time. arXiv:gr-qc/9210011 (1992)
  18. 18.
    Kadic, A., Edelen, D.G.B.: A Gauge Theory of Dislocations and Disclinations. Lecture Notes in Physics, vol. 174. Springer, Berlin (1983) MATHGoogle Scholar
  19. 19.
    Kähler, E.: Rendiconti Mat. 21(3–4), 425 (1962). See also Ivanenko, D., Landau, L., Z. Phys. 48, 341 (1928) Google Scholar
  20. 20.
    Kogut, J., Susskind, L.: PRD 11, 395 (1975) CrossRefADSGoogle Scholar
  21. 21.
    Pati, J.C., Salam, A.: Lepton number as the fourth color. Phys. Rev. D 10, 275 (1974) CrossRefADSGoogle Scholar
  22. 22.
  23. 23.
    Preskill, J.: Do black holes destroy information? arXiv:hep-th/9209058 (1992)
  24. 24.
    Rabin, J.M.: Nucl. Phys. B 201, 315 (1982) CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    Schmelzer, I.: A generalization of the Lorentz ether to gravity with general-relativistic limit. arXiv:gr-qc/0205035 (2002)
  26. 26.
    Susskind, L.: Phys. Rev. D 16, 3031 (1977) CrossRefADSGoogle Scholar
  27. 27.
    Volovik, G.E.: Induced gravity in superfluid 3He. arXiv:cond-mat/9806010 (1998)
  28. 28.
    Wheeler, J.A.: Geometrodynamica. Academic Press, New York (1962) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.BerlinGermany

Personalised recommendations