Skip to main content
SpringerLink
Log in
Book cover

Planck Scale Effects in Astrophysics and Cosmology pp 131–159Cite as

Introduction to Doubly Special Relativity

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Physics ((LNP,volume 669))

Abstract

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.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Amelino-Camelia, “Testable scenario for relativity with minimum-length,” Phys. Lett. B 510, 255 (2001) [arXiv:hep-th/0012238].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  3. J. Kowalski-Glikman, “Observer independent quantum of mass,” Phys. Lett. A 286, 391 (2001) [arXiv:hep-th/0102098].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  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. J. E. Nelson, T. Regge and F. Zertuche, “Homotopy Groups And (2+1)-Dimensional Quantum De Sitter Gravity,” Nucl. Phys. B 339 (1990) 516.

    Article  Google Scholar 

  7. S. Majid, Introduction to Quantum Groups, Cambridge University Press, 1995.

    Google Scholar 

  8. A. Agostini, G. Amelino-Camelia and F. D';Andrea, “Hopf-algebra description of noncommutative-spacetime symmetries,” arXiv:hep-th/0306013.

    Google Scholar 

  9. A. O. Barut and R. Raczka, Theory of Group Representations and Applications, PWN, Warsaw, 1977.

    Google Scholar 

  10. J. Lukierski, H. Ruegg, A. Nowicki and V. N. Tolstoi, “Q deformation of Poincare algebra,” Phys. Lett. B 264 (1991) 331.

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  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. L. Smolin, “Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity,” J. Math. Phys. 36 (1995) 6417 [arXiv:gr-qc/9505028].

    Article  Google Scholar 

  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. S. Major, L. Smolin, “Quantum deformation of quantum gravity,” Nucl.Phys. B473 (1996) 267 [arXiv:gr-qc/9512020].

    Article  Google Scholar 

  16. A. Starodubtsev, “Topological excitations around the vacuum of quantum gravity I: the symmetries of the vacuum,” hep-th/0306135.

    Google Scholar 

  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. J. Kowalski-Glikman, “De Sitter space as an arena for doubly special relativity,” Phys. Lett. B 547 (2002) 291 [arXiv:hep-th/0207279].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  20. J. Kowalski-Glikman and S. Nowak, “Doubly special relativity and de Sitter space,” Class. Quant. Grav. 20 (2003) 4799 [arXiv:hep-th/0304101].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  25. D. V. Ahluwalia-Khalilova, “Operational indistinguishabilty of doubly special relativities from special relativity,” arXiv:gr-qc/0212128.

    Google Scholar 

  26. J. Magueijo and L. Smolin, “Lorentz invariance with an invariant energy scale,” Phys. Rev. Lett. 88 (2002) 190403 [arXiv:hep-th/0112090].

    Article  PubMed  Google Scholar 

  27. J. Magueijo and L. Smolin, “Generalized Lorentz invariance with an invariant energy scale,” Phys. Rev. D 67 (2003) 044017 [arXiv:gr-qc/0207085].

    Article  Google Scholar 

  28. H. S. Snyder, “Quantized Space-Time,” Phys. Rev. 71 (1947) 38.

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  30. D. Kimberly, J. Magueijo and J. Medeiros, “Non-Linear Relativity in Position Space,” arXiv:gr-qc/0303067.

    Google Scholar 

  31. A. A. Kirillov, Elements of the Theory of Representations, Springer 1976.

    Google Scholar 

  32. A. Yu. Alekseev and A. Z. Malkin, “Symplectic structures associated with Lie-Poisson groups”, Comm. Math. Phys. 162 (1994) 147.

    Google Scholar 

  33. P. Kosinski and P. Maslanka, “The κWeyl group and its algebra”, arXiv:q-alg/9512018.

    Google Scholar 

  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. 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].

    Article  Google Scholar 

  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. 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].

    Article  Google Scholar 

  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. 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. G. Amelino-Camelia, “Quantum-gravity phenomenology: Status and prospects,” Mod. Phys. Lett. A 17 (2002) 899 [arXiv:gr-qc/0204051].

    Article  Google Scholar 

  41. G. Amelino-Camelia, J. Kowalski-Glikman, G. Mandanici and A. Procaccini, “Phenomenology of doubly special relativity,” arXiv:gr-qc/0312124.

    Google Scholar 

  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].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  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. 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].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  48. P. Kosinski and P. Maslanka, “Deformed Galilei symmetry,” [arXiv:math.QA/ 9811142].

    Google Scholar 

  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].

    Article  PubMed  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Wroclaw, Wroclaw

    J. Kowalski-Glikman

Authors
  1. J. Kowalski-Glikman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jurek Kowalski-Glikman Giovanni Amelino-Camelia

Rights and permissions

Reprints and permissions

About this chapter

Cite this chapter

Kowalski-Glikman, J. Introduction to Doubly Special Relativity. In: Kowalski-Glikman, J., Amelino-Camelia, G. (eds) Planck Scale Effects in Astrophysics and Cosmology. Lecture Notes in Physics, vol 669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11377306_5

Download citation

Publish with us

Policies and ethics

Search

Navigation