Introduction to Doubly Special Relativity

  • J. Kowalski-Glikman
Part of the Lecture Notes in Physics book series (LNP, volume 669)


What is the fate of Lorentz symmetry at Planck scale? This question was the main theme of the Winter School and, as the reader could see from the proceedings, there are many possible answers. Here I would like to describe one possibility, whose central postulate is that in spite of the fact that departures from Special Relativity are introduced at scales close to Planck scale, one keeps unchanged the central physical message of the theory of relativity, namely the equivalence of all (inertial) observers. This justifies the term Relativity in the title.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. Amelino-Camelia, “Testable scenario for relativity with minimum-length,” Phys. Lett. B 510, 255 (2001) [arXiv:hep-th/0012238].CrossRefGoogle Scholar
  2. 2.
    G. Amelino-Camelia, “Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale,” Int. J. Mod. Phys. D 11, 35 (2002) [arXiv:gr-qc/0012051].CrossRefGoogle Scholar
  3. 3.
    J. Kowalski-Glikman, “Observer independent quantum of mass,” Phys. Lett. A 286, 391 (2001) [arXiv:hep-th/0102098].CrossRefGoogle Scholar
  4. 4.
    N. R. Bruno, G. Amelino-Camelia and J. Kowalski-Glikman, “Deformed boost transformations that saturate at the Planck scale,” Phys. Lett. B 522, 133 (2001) [arXiv:hep-th/0107039].CrossRefGoogle Scholar
  5. 5.
    G. Amelino-Camelia, L. Smolin and A. Starodubtsev, “Quantum symmetry, the cosmological constant and Planck scale phenomenology,” arXiv:hep-th/0306134.Google Scholar
  6. 6.
    J. E. Nelson, T. Regge and F. Zertuche, “Homotopy Groups And (2+1)-Dimensional Quantum De Sitter Gravity,” Nucl. Phys. B 339 (1990) 516.CrossRefGoogle Scholar
  7. 7.
    S. Majid, Introduction to Quantum Groups, Cambridge University Press, 1995.Google Scholar
  8. 8.
    A. Agostini, G. Amelino-Camelia and F. D';Andrea, “Hopf-algebra description of noncommutative-spacetime symmetries,” arXiv:hep-th/0306013.Google Scholar
  9. 9.
    A. O. Barut and R. Raczka, Theory of Group Representations and Applications, PWN, Warsaw, 1977.Google Scholar
  10. 10.
    J. Lukierski, H. Ruegg, A. Nowicki and V. N. Tolstoi, “Q deformation of Poincare algebra,” Phys. Lett. B 264 (1991) 331.CrossRefGoogle Scholar
  11. 11.
    J. Lukierski, A. Nowicki and H. Ruegg, “Real forms of complex quantum anti-De Sitter algebra Uq(Sp(4:C)) and their contraction schemes,” Phys. Lett. B 271 (1991) 321 [arXiv:hep-th/9108018].CrossRefGoogle Scholar
  12. 12.
    S. Majid and H. Ruegg, “Bicrossproduct structure of kappa Poincare group and noncommutative geometry,” Phys. Lett. B 334 (1994) 348 [arXiv:hep-th/9405107]; J. Lukierski, H. Ruegg and W. J. Zakrzewski, “Classical quantum mechanics of free kappa relativistic systems,” Annals Phys. 243 (1995) 90 [arXiv:hep-th/9312153].Google Scholar
  13. 13.
    L. Smolin, “Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity,” J. Math. Phys. 36 (1995) 6417 [arXiv:gr-qc/9505028].CrossRefGoogle Scholar
  14. 14.
    J. C. Baez, “An Introduction to Spin Foam Models of Quantum Gravity and BF Theory,” Lect. Notes Phys. 543 (2000) 25 [arXiv:gr-qc/9905087].Google Scholar
  15. 15.
    S. Major, L. Smolin, “Quantum deformation of quantum gravity,” Nucl.Phys. B473 (1996) 267 [arXiv:gr-qc/9512020].CrossRefGoogle Scholar
  16. 16.
    A. Starodubtsev, “Topological excitations around the vacuum of quantum gravity I: the symmetries of the vacuum,” hep-th/0306135.Google Scholar
  17. 17.
    L. Freidel and D. Louapre, “Ponzano-Regge model revisited. I: Gauge fixing, observables and interacting spinning particles,” arXiv:hep-th/0401076.Google Scholar
  18. 18.
    J. Kowalski-Glikman, “De Sitter space as an arena for doubly special relativity,” Phys. Lett. B 547 (2002) 291 [arXiv:hep-th/0207279].CrossRefGoogle Scholar
  19. 19.
    J. Kowalski-Glikman and S. Nowak, “Doubly special relativity theories as different bases of kappa-Poincare algebra,” Phys. Lett. B 539 (2002) 126 [arXiv:hep-th/0203040].CrossRefGoogle Scholar
  20. 20.
    J. Kowalski-Glikman and S. Nowak, “Doubly special relativity and de Sitter space,” Class. Quant. Grav. 20 (2003) 4799 [arXiv:hep-th/0304101].CrossRefGoogle Scholar
  21. 21.
    J. Kowalski-Glikman and S. Nowak, “Non-commutative space-time of doubly special relativity theories,” Int. J. Mod. Phys. D 12 (2003) 299 [arXiv:hep-th/0204245].CrossRefGoogle Scholar
  22. 22.
    L. Freidel, J. Kowalski-Glikman and L. Smolin, “2+1 gravity and doubly special relativity,” Phys. Rev. D 69 (2004) 044001 [arXiv:hep-th/0307085].CrossRefGoogle Scholar
  23. 23.
    H. J. Matschull and M. Welling, “Quantum mechanics of a point particle in 2+1 dimensional gravity,” Class. Quant. Grav. 15 (1998) 2981 [arXiv:gr-qc/9708054].CrossRefGoogle Scholar
  24. 24.
    J. Lukierski and A. Nowicki, “Doubly Special Relativity versus κ-deformation of relativistic kinematics,” Int. J. Mod. Phys. A 18 (2003) 7 [arXiv:hep-th/0203065].CrossRefGoogle Scholar
  25. 25.
    D. V. Ahluwalia-Khalilova, “Operational indistinguishabilty of doubly special relativities from special relativity,” arXiv:gr-qc/0212128.Google Scholar
  26. 26.
    J. Magueijo and L. Smolin, “Lorentz invariance with an invariant energy scale,” Phys. Rev. Lett. 88 (2002) 190403 [arXiv:hep-th/0112090].CrossRefPubMedGoogle Scholar
  27. 27.
    J. Magueijo and L. Smolin, “Generalized Lorentz invariance with an invariant energy scale,” Phys. Rev. D 67 (2003) 044017 [arXiv:gr-qc/0207085].CrossRefGoogle Scholar
  28. 28.
    H. S. Snyder, “Quantized Space-Time,” Phys. Rev. 71 (1947) 38.CrossRefGoogle Scholar
  29. 29.
    P. Kosinski, J. Lukierski, P. Maslanka and J. Sobczyk, “The Classical basis for kappa deformed Poincare (super)algebra and the second kappa deformed supersymmetric Casimir,” Mod. Phys. Lett. A 10 (1995) 2599 [arXiv:hep-th/9412114].CrossRefGoogle Scholar
  30. 30.
    D. Kimberly, J. Magueijo and J. Medeiros, “Non-Linear Relativity in Position Space,” arXiv:gr-qc/0303067.Google Scholar
  31. 31.
    A. A. Kirillov, Elements of the Theory of Representations, Springer 1976.Google Scholar
  32. 32.
    A. Yu. Alekseev and A. Z. Malkin, “Symplectic structures associated with Lie-Poisson groups”, Comm. Math. Phys. 162 (1994) 147.Google Scholar
  33. 33.
    P. Kosinski and P. Maslanka, “The κWeyl group and its algebra”, arXiv:q-alg/9512018.Google Scholar
  34. 34.
    J. Lukierski and A. Nowicki, “ Heisenberg double description of κ-Poincar&x00027;e algebra and κ-deformed phase space”, Proceedings of Quantum Group Symposium at Group 21, (July 1996, Goslar) Eds. H.-D. Doebner and V.K. Dobrev, Heron Press, Sofia, 1997, p. 186, [arXiv:q-alg/9702003].Google Scholar
  35. 35.
    A. Blaut, M. Daszkiewicz, J. Kowalski-Glikman and S. Nowak, “Phase spaces of doubly special relativity,” Phys. Lett. B 582 (2004) 82 [arXiv:hep-th/0312045].CrossRefGoogle Scholar
  36. 36.
    P. Kosinski, P. Maslanka, J. Lukierski and A. Sitarz, “Generalized kappa-deformations and deformed relativistic scalar fields on noncommutative Minkowski space,” arXiv:hep-th/0307038.Google Scholar
  37. 37.
    G. Amelino-Camelia and M. Arzano, “Coproduct and star product in field theories on Lie-algebra non-commutative space-times,” Phys. Rev. D 65 (2002) 084044 [arXiv:hep-th/0105120].CrossRefGoogle Scholar
  38. 38.
    G. Amelino-Camelia, M. Arzano and L. Doplicher, “Field theories on canonical and Lie-algebra noncommutative spacetimes,” arXiv:hep-th/0205047.Google Scholar
  39. 39.
    V. G. Kadyshevsky et. al., “Quantum field theory and a new universal high-energy scale”, Nuovo Cim. 87 A (1985) 324; Nuovo Cim. 87 A (1985) 350; Nuovo Cim. 87 A (1985) 373, and references therein.Google Scholar
  40. 40.
    G. Amelino-Camelia, “Quantum-gravity phenomenology: Status and prospects,” Mod. Phys. Lett. A 17 (2002) 899 [arXiv:gr-qc/0204051].CrossRefGoogle Scholar
  41. 41.
    G. Amelino-Camelia, J. Kowalski-Glikman, G. Mandanici and A. Procaccini, “Phenomenology of doubly special relativity,” arXiv:gr-qc/0312124.Google Scholar
  42. 42.
    G. Amelino-Camelia and S. Majid, “Waves on noncommutative spacetime and gamma-ray bursts,” Int. J. Mod. Phys. A 15 (2000) 4301 [arXiv:hep-th/9907110].CrossRefGoogle Scholar
  43. 43.
    T. Tamaki, T. Harada, U. Miyamoto and T. Torii, “Particle velocity in noncommutative space-time,” Phys. Rev. D 66 (2002) 105003 [arXiv:gr-qc/0208002].CrossRefGoogle Scholar
  44. 44.
    G. Amelino-Camelia, F. D'Andrea and G. Mandanici, “Group velocity in noncommutative spacetime,” JCAP 0309 (2003) 006 [arXiv:hep-th/0211022].Google Scholar
  45. 45.
    M. Daszkiewicz, K. Imilkowska and J. Kowalski-Glikman, “Velocity of particles in doubly special relativity,” Phys. Lett. A 323 (2004) 345 [arXiv:hep-th/0304027].CrossRefGoogle Scholar
  46. 46.
    P. Kosinski and P. Maslanka, “On the definition of velocity in doubly special relativity theories,” Phys. Rev. D 68 (2003) 067702 [arXiv:hep-th/0211057].CrossRefGoogle Scholar
  47. 47.
    S. Mignemi, “On the definition of velocity in theories with two observer-independent scales,” Phys. Lett. A 316 (2003) 173 [arXiv:hep-th/0302065].CrossRefGoogle Scholar
  48. 48.
    P. Kosinski and P. Maslanka, “Deformed Galilei symmetry,” [arXiv:math.QA/ 9811142].Google Scholar
  49. 49.
    F. Bonechi, E. Celeghini, R. Giachetti, E. Sorace and M. Tarlini, “Inhomogeneous Quantum Groups As Symmetries Of Phonons,” Phys. Rev. Lett. 68 (1992) 3718 [arXiv:hep-th/9201002].CrossRefPubMedGoogle Scholar
  50. 50.
    G. Amelino-Camelia, “Are we at the dawn of quantum-gravity phenomenology?,” Lect. Notes Phys. 541 (2000) 1 [arXiv:gr-qc/9910089].Google Scholar

Authors and Affiliations

  • J. Kowalski-Glikman
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of WroclawWroclaw

Personalised recommendations