Skip to main content
SpringerLink
Log in

Phenomenology of the Noncommutative Standard Model

  • Chapter
  • First Online:
Book cover Noncommutative Geometry and Particle Physics

Part of the book series: Mathematical Physics Studies ((MPST))

  • 2010 Accesses

Abstract

>In Theorems 11.10 and 11.11, we have derived the full Lagrangian for the Standard Model from the almost-commutative manifold \(M\times F_{\scriptscriptstyle SM}\).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 64.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Chamseddine, A.H., Connes, A., Marcolli, M.: Gravity and the standard model with neutrino mixing. Adv. Theory Math. Phys. 11, 991–1089 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Connes, A., Marcolli, M.: Noncommutative Geometry. Quantum Fields and Motives. AMS, Providence (2008)

    Google Scholar 

  3. Jureit, J., Krajewski, T., Schücker, T., Stephan, C.A.: Seesaw and noncommutative geometry. Phys. Lett. B 654, 127–132 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. van den Dungen, K., van Suijlekom, W.D.: Particle physics from almost commutative spacetimes. Rev. Math. Phys. 24, 1230004 (2012)

    Article  MathSciNet  Google Scholar 

  5. Mohapatra, R., Pal, P.: Massive neutrinos in physics and astrophysics, 2nd edn. World Sci. Lect. Notes Phys. 60, 1–397 (1998)

    Google Scholar 

  6. Machacek, M., Vaughn, M.: Two-loop renormalization group equations in a general quantum field theory: (i) wave function renormalization. Nucl. Phys. B 222, 83–103 (1983)

    Article  ADS  Google Scholar 

  7. Machacek, M., Vaughn, M.: Two-loop renormalization group equations in a general quantum field theory: (ii) Yukawa couplings. Nucl. Phys. B 236, 221–232 (1984)

    Article  ADS  Google Scholar 

  8. Machacek, M., Vaughn, M.: Two-loop renormalization group equations in a general quantum field theory: (iii) Scalar quartic couplings. Nucl. Phys. B 249, 70–92 (1985)

    Article  ADS  Google Scholar 

  9. Ford, C., Jones, D.R.T., Stephenson, P.W., Einhorn, M.B.: The effective potential and the renormalisation group. Nucl. Phys. B 395, 17–34 (1993)

    Article  ADS  Google Scholar 

  10. Nakamura, K., et al.: Review of particle physics. J. Phys. G: Nucl. Part. Phys. 37, 075021 (2010)

    Article  ADS  Google Scholar 

  11. Appelquist, T., Carazzone, J.: Infrared singularities and massive fields. Phys. Rev. D 11, 2856–2861 (1975)

    Article  ADS  Google Scholar 

  12. Antusch, S., Kersten, J., Lindner, M., Ratz, M.: Neutrino mass matrix running for non-degenerate see-saw scales. Phys. Lett. B 538, 87–95 (2002)

    Article  ADS  Google Scholar 

  13. Aad, G., et al.: Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B716, 1–29 (2012)

    Article  ADS  Google Scholar 

  14. Chatrchyan, S., et al.: Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B716, 30–61 (2012)

    Article  ADS  Google Scholar 

  15. Essouabri, D., Iochum, B., Levy, C., Sitarz, A.: Spectral action on noncommutative torus. J. Noncommut. Geom. 2, 53–123 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  16. Gayral, V., Lochum, B.: The spectral action for Moyal planes. J. Math. Phys. 46(043503), 17 (2005)

    Google Scholar 

  17. Grosse, H., Wulkenhaar, R.: 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory. J. Geom. Phys. 62, 1583–1599 (2012)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. Iochum, B., Levy, C., Sitarz, A.: Spectral action on \(SU_q(2)\). Commun. Math. Phys. 289, 107–155 (2009)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. Eckstein, M., Lochum, B., Sitarz, A.: Heat trace and spectral action on the standard Podles sphere. Commun. Math. Phys. (published online: 6 May 2014)

    Google Scholar 

  20. Farnsworth, S., Boyle, L.: Non-associative geometry and the spectral action principle. arXiv:1303.1782

  21. Boyle, L., Farnsworth, S.: Non-commutative geometry, non-associative geometry and the standard model of particle, physics. arXiv:1401.5083

  22. Chamseddine, A.H., Connes, A.: Universal formula for noncommutative geometry actions: unifications of gravity and the standard model. Phys. Rev. Lett. 77, 4868–4871 (1996)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  23. Wilson, K.G.: Renormalization group methods. Adv. Math. 16, 170–186 (1975)

    Article  Google Scholar 

  24. Iochum, B., Levy, C., Vassilevich, D.: Spectral action beyond the weak-field approximation. Commun. Math. Phys. 316, 595–613 (2012)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  25. Iochum, B., Levy, C., Vassilevich, D.: Global and local aspects of spectral actions. J. Phys. A45, 374020 (2012)

    MathSciNet  Google Scholar 

  26. Kurkov, M., Lizzi, F., Vassilevich, D.: High energy bosons do not propagate. Phys. Lett. B731, 311–315 (2014)

    Google Scholar 

  27. van Suijlekom, W.D.: Renormalization of the spectral action for the Yang-Mills system. JHEP 1103, 146 (2011)

    Article  ADS  Google Scholar 

  28. van Suijlekom, W.D.: Renormalization of the asymptotically expanded Yang-Mills spectral action. Commun. Math. Phys. 312, 883–912 (2012)

    Article  MATH  ADS  Google Scholar 

  29. van Suijlekom, W.D.: Renormalizability conditions for almost commutative manifolds. Ann. H. Poincaré 15, 985–1011 (2014)

    Google Scholar 

  30. van Suijlekom, W.D.: Renormalizability conditions for almost-commutative geometries. Phys. Lett. B711, 434–438 (2012)

    Article  ADS  Google Scholar 

  31. Stephan, C.A.: Almost-commutative geometries beyond the standard model. J. Phys. A39, 9657 (2006)

    ADS  Google Scholar 

  32. Stephan, C.A.: Almost-commutative geometries beyond the Standard Model. ii. new colours. J. Phys. A40, 9941 (2007)

    ADS  Google Scholar 

  33. Stephan, C.A.: New scalar fields in noncommutative geometry. Phys. Rev. D79, 065013 (2009)

    ADS  Google Scholar 

  34. Stephan, C.A.: Beyond the standard model: a noncommutative approach. arXiv:0905.0997

  35. Stephan, C.A.: A dark sector extension of the almost-commutative standard model. Int. J. Mod. Phys. A29, 1450005 (2014)

    Article  ADS  Google Scholar 

  36. van den Broek, T., van Suijlekom, W.D.: Supersymmetric QCD and noncommutative geometry. Commun. Math. Phys. 303, 149–173 (2011)

    Article  MATH  ADS  Google Scholar 

  37. van den Broek, T., van Suijlekom, W.D.: Supersymmetric QCD from noncommutative geometry. Phys. Lett. B699, 119–122 (2011)

    Article  ADS  Google Scholar 

  38. Beenakker, W., van den Broek, T., van Suijlekom, W.: Noncommutative and supersymmetry. Part I: supersymmetric almost-commutative geometries (to appear)

    Google Scholar 

  39. Beenakker, W., van den Broek, T., van Suijlekom, W.: Noncommutative and supersymmetry. Part II: supersymmetry breaking (to appear)

    Google Scholar 

  40. Beenakker, W., van den Broek, T., van Suijlekom, W.: Noncommutative and supersymmetry. Part III: the noncommutative supersymmetric standard model (to appear)

    Google Scholar 

  41. Estrada, C., Marcolli, M.: Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models. Int. J. Geom. Meth. Mod. Phys. 10, 1350036 (2013)

    Article  MathSciNet  Google Scholar 

  42. Sher, M.: Electroweak Higgs potentials and vacuum stability. Phys. Rept. 179, 273–418 (1989)

    Article  ADS  Google Scholar 

  43. Chamseddine, A.H., Connes, A.: Resilience of the spectral standard model. JHEP 1209, 104 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  44. Chamseddine, A.H., Connes, A.: Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I. Fortsch. Phys. 58, 553–600 (2010)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  45. Ćaćić, B.: A reconstruction theorem for almost-commutative spectral triples. Lett. Math. Phys. 100, 181–202 (2012)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  46. Ćaćić, B.: Real structures on almost-commutative spectral triples. Lett. Math. Phys. 103, 793–816 (2013)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  47. Boeijink, J., van den Dungen, K.: Notes on topologically non-trivial almost-commutative geometries. arXiv:1405.5368

  48. Pati, J.C., Salam, A.: Lepton number as the fourth color. Phys. Rev. D10, 275–289 (1974)

    ADS  Google Scholar 

  49. Chamseddine, A.H., Connes, A., Van Suijlekom, W.D.: Inner fluctuations in noncommutative geometry without the first order condition. J. Geom. Phys. 73, 222–234 (2013)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  50. Chamseddine, A.H., Connes, A., van Suijlekom, W.D.: Beyond the spectral standard model: emergence of Pati-Salam unification. JHEP 1311, 132 (2013)

    Article  ADS  Google Scholar 

  51. Devastato, A., Lizzi, F., Martinetti, P.: Grand symmetry, spectral action, and the Higgs mass. JHEP 1401, 042 (2014)

    Article  ADS  Google Scholar 

  52. Chamseddine, A.H., Connes, A.: Why the standard model. J. Geom. Phys. 58, 38–47 (2008)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  53. Gonderinger, M., Li, Y., Patel, H., Ramsey-Musolf, M.J.: Vacuum stability, perturbativity, and scalar singlet dark matter. JHEP 1001, 053 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands

    Walter D. van Suijlekom

Authors
  1. Walter D. van Suijlekom
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Walter D. van Suijlekom .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

van Suijlekom, W.D. (2015). Phenomenology of the Noncommutative Standard Model. In: Noncommutative Geometry and Particle Physics. Mathematical Physics Studies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9162-5_12

Download citation

Publish with us

Policies and ethics

Search

Navigation