Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
권호 표지

THE RELATIONSHIP BETWEEN NONCOMMUTATIVE AND LORENTZVIOLATING PARAMETERS IN QUANTUM

  • HEIDARI, A. (INSTITUTE FOR ADVANCED STUDIES) ;
  • GHORBANI, F. (INSTITUTE FOR ADVANCED STUDIES) ;
  • GHORBANI, M. (INSTITUTE FOR ADVANCED STUDIES)
  • Received : 2012.06.18
  • Accepted : 2012.09.14
  • Published : 2012.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

When it comes to Lorentz symmetry violation, there are generally two approaches to studying noncommutative field theory: 1) conventional fields are equivalent to noncommutative fields; however, symmetry groups are larger. 2) The symmetry group is the same as conventional standard model's symmetry group; but fields here are written based on the Seiberg-Witten map. Here by adopting the first approach, we aim to connect Lorentz violation coefficients with noncommutative parameters and compare the results with the second approach's results. Through the experimental values obtained for the Lorentz-violating parameters, we obtain a limit of noncommutative symmetry.

Keywords

Acknowledgement

The work described in this paper was fully supported by grants from the Institute for Advanced Studies of Iran. The authors would like to express genuinely and sincerely thanks and appreciated and their gratitude to Institute for Advanced Studies of Iran.

References

  1. O. W. Greenberg, CPT Violation Implies Violation of Lorentz Invariance, Phys. Rev. Lett. 89 (2002) 2316021. https://doi.org/10.1103/PhysRevLett.89.231602
  2. D. Colladay and V. A. Kostelecky, CPT violation and the standard model, Phys. Rev. D. 55 (1997) 6760. https://doi.org/10.1103/physrevd.55.6760
  3. R. Lehnert, CPT and Lorentz violation as signatures for Planck-scale physics, J. Phys, Conf. Ser. 171 (2009) 012036. https://doi.org/10.1088/1742-6596/171/1/012036
  4. D. Colladay and V. A. Kostelecky, Lorentz-violating extension of the standard model, Phys. Rev. D. 58 (1998) 116002. https://doi.org/10.1103/physrevd.58.116002
  5. V. A. Kostelecky and N. Russell, Data Tables for Lorentz and CPT Violation, hep-ph: 0801.0287 (2008).
  6. V. A. Kostelecky and C. Lane, Constraints on Lorentz violation from clock-comparison experiments, hepph/9908504v1 (1999).
  7. P. Wolf, F. Chapelet, S. Bize, and A. Clairon, Cold Atom Clock Test of Lorentz Invariance in the Matter Sector, Phys. Rev. Lett. 96, 060801(2006). https://doi.org/10.1103/PhysRevLett.96.060801
  8. R. Bluhm,V. A. Kostelecky, and N. Russell., Searching for Lorentz Violation in the Ground State of Hydrogen, hep-ph/ 0003223 (2006).
  9. P. L. Stanwix, M.E. Tobar, P. Wolf, C.R. Locke, and E.N. Ivanov, Improved test of Lorentz invariance in electrodynamics using rotating cryogenic sapphire oscillators, Phys. Rev. D 74 (2006) 081101. https://doi.org/10.1103/physrevd.74.081101
  10. L. B. Auerbach et al., Tests of Lorentz violation in ν̅μ→ν̅e oscillations, Phys. Rev. D 72 (2005) 076004. https://doi.org/10.1103/physrevd.72.076004
  11. C. P. Martin, D. Sanchez-Ruiz, and C. Tamarit, The noncommutative U(1) Higgs-Kibble model in the enveloping-algebra formalism and its renormalizability, JHEP. 02 (2007) 065.
  12. S. M. Carroll, J. A. Harvey, V. A. Kostelecky, C. D. Lane, and T. Okamoto, Noncommutative Field Theory and Lorentz Violation, Phys. Rev. Lett. 84 (2001) 141601.
  13. M. Hayakawa, Perturbative analysis on infrared aspects of noncommutative QED on R4, Phys. Lett. B 478(2000) 394. https://doi.org/10.1016/S0370-2693(00)00242-2
  14. A. Alboteanu, T. Ohl, and R. Ruckl, Probing the noncommutative standard model at hadron colliders, Phys. Rev. D 74 (2006) 096004. https://doi.org/10.1103/physrevd.74.096004
  15. X. Calmet, B. Jurco, P. Schupp, J. Wess, and M. Wohlgenannt, The standard model on non-commutative space-time, Eur. Phys. J. C 23 (2002) 363. https://doi.org/10.1007/s100520100873
  16. N. Seiberg and E. Witten, String Theory and Noncommutative Geometry, JHEP. 032 (1999) 9909.
  17. L. Moller, Second order expansion of action functionals of noncommutative gauge theories, JHEP. 10 (2004) 063.
  18. B. Jurco, L. Moller, S. Schraml, P. Schupp and J. Wess, Construction of non-Abelian gauge theories on noncommutative spaces, Eur. Phys. J. C 21 (2001) 383. https://doi.org/10.1007/s100520100731
  19. M. Moumni, A. BenSlama, and S. Zaim, A new limit for the noncommutative space-time parameter, Journal of Geometry and Physic, 61, 1 (2011) 151-156. https://doi.org/10.1016/j.geomphys.2010.09.010
  20. V. A. Kostelecky and M. Mewes, Lorentz-Violating Electrodynamics and the Cosmic Microwave Background, Phys. Rev. Lett. 99 (2007) 011601. https://doi.org/10.1103/PhysRevLett.99.011601
  21. A. Kostelecky and C. Lane, Constraints on Lorentz violation from clock-comparison experiments, Phys. Rev. D 60 (1999) 116010. https://doi.org/10.1103/physrevd.60.116010
  22. H. Muller, S. Herrmann, A. Saenz, A. Peters, and C. Lammerzahl, Optical cavity tests of Lorentz invariance for the electron, Phys. Rev. D 68 (2003) 116006. https://doi.org/10.1103/PhysRevD.68.116006
  23. H. Muller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, Tests of Relativity by Complementary Rotating Michelson-Morley Experiments, Phys. Rev. Lett. 99 (2007) 050401. https://doi.org/10.1103/physrevlett.99.050401
  24. B. Altschul, Testing Electron Boost Invariance with 2S-1S Hydrogen Spectroscopy, arxiv:0912.0530.
  25. V. A. Kostelecky and M. Mewes, Signals for Lorentz violation in electrodynamics, Phys. Rev. D 66 (2002) 056005. https://doi.org/10.1103/physrevd.66.056005
  26. V. A. Kostelecky and M. Mewes, Sensitive Polarimetric Search for Relativity Violations in Gamma-Ray Bursts, Phys. Rev. Lett. 97 (2006) 140401. https://doi.org/10.1103/PhysRevLett.97.140401
  27. S. Herrmann, A. Senger, K. Mohle, M. Nagel, E. V. Kovalchuk, and A. Peters, Rotating optical cavity experiment testing Lorentz invariance at the 10-17 level, Phys. Rev. D 80 (2009) 105011. https://doi.org/10.1103/physrevd.80.105011
  28. V. A. Kostelecky, C. D. Lane, and A. G. M. Pickering, One-loop renormalization of Lorentz-violating electrodynamics, Phys. Rev. D 65 (2002) 056006. https://doi.org/10.1103/physrevd.65.056006