Croatian Science Foundation Research Project

Project: Towards quantum gravity: noncomutative geometry, field theory and cosmology

Principal Investigator (PI): Stjepan Meljanac, - senior scientist, Rudjer Bošković Institute (RBI)

Starting date: 1.09.2015.

Ending date: 31.8.2017.

Project proposal summary

The proposed project aims at carrying out research on various aspects of quantum gravity, related areas of mathematical physics, certain topics in cosmology, astroparticle physics and physics of black holes. Whereas a satisfactory theory of quantum gravity still remains elusive, some of the assessed properties revealing a nonlocal character of such a theory (i.e. noncommutativity of spacetime coordinates, ultraviolet/infrared (UV/IR) mixing and the holographic principle) has already changed our perspective upon reconciliation of the quantum field theory (QFT) framework with general relativity. A particular attention will be paid to construction, classification and unification of noncomutative (NC) spaces. In this regard, a procedure can be defined by making use of rigorous quantum deformation techniques as well as some well-known differential algebra concepts such as the Hopf algebra. This permits formulation and study of the twist-deformed Riemannian geometry, the twisted version of Einstein's equations and the algebraic structure on kappa-deformed Minkowski space. A further extension of these ideas opens a possibility to study NC effect in black holes. Furthermore, using the tools of QFT in curved spacetime, several aspects of modern cosmology will be covered including those based on the most successful realization of the holographic principle - the AdS/CFT duality. Finally, a class of quantum gravity models will be tested by probing Lorentz violation in observations of rapidly-varying astrophysical sources of high-energy gamma-rays. This requires a full-fledged field-theoretical model with a trouble-free and meaningful quantum loop results, with all UV and IR pathologies being under control.

Objectives of the proposed research

  1. NC differential geometry on deformed spaces
  2. NC metric
  3. NC fields in BTZ background
  4. NC gravity
  5. NC physics and near horizon geometries
  6. θ-exact covariant NCQFT
  7. New couplings/new processes
  8. Limit on the non-commutative scale
  9. Application to Astroparticle physics
  10. Hadronic fluid and AdS/CFT
  11. K-essence unification and De Sitter invariant propagators


  1. T. Jurić, S. Meljanac, D. Pikutić and R. Štrajn,"Toward the classification of differential calculi on κ-Minkowski space and related field theories", JHEP 1507, 055 (2015), arXiv:1502.02972.
  2. R. Horvat, "Avoiding Boltzmann Brain domination in holographic dark energy models", Phys.Lett. B 750, 181 (2015), arXiv:1502.06348.
  3. T. Jurić, S. Meljanac and A. Samsarov, "Light-like κ-deformations and scalar field theory via Drinfeld twist", J.Phys.Conf.Ser. 634, no. 1, 012005 (2015), arXiv:1506.02475.
  4. R. Horvat, J. Trampetić and J. You, "Photon polarization tensor on deformed spacetime: A four-photon-tadpole contribution", Phys. Rev. D 92, 125006 (2015), arXiv:1506.02864.
  5. T. Juric, S. Meljanac and D. Pikutić, "Realizations of kappa-Minkowski space, Drinfeld twists and related symmetry algebras", Eur. Phys. J. C 75, no. 11, 528 (2015), arXiv:1506.04955.
  6. A. Géré, T. Jurić and J. C. Wallet, "Noncommutative gauge theories on ${\mathrm{\mathbb{R}}}_{\lambda}^3$: perturbatively finite models", JHEP 1512, 045 (2015), arXiv:1507.08086.
  7. S. Meljanac, A. Pachoł and D. Pikutić, "Twisted conformal algebra related to kappa-Minkowski space", Phys. Rev. D 92, no. 10, 105015 (2015), arXiv:1509.02115.
  8. R. Horvat, J. Trampetić and J. You, "Photon self-interaction on deformed spacetime", Phys. Rev. D 92, no. 12, 125006 (2015), 125006 (2015), arXiv:1510.08691.
  9. S. Meljanac, S. Krešić-Jurić and T. Martinić, "The Weyl realizations of Lie algebras and left-right duality, arXiv:1511.03936 [math-ph].
  10. T. Jurić, S. Meljanac and A. Samsarov, "Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics", arXiv:1511.05592 [hep-th].
  11. N. Bilić, "Randall-Sundrum versus holographic cosmology", Phys. Rev. D 93, no. 6, 066010 (2016), arXiv:1511.07323.
  12. A. Borowiec, T. Juric, S. Meljanac, A. Pachoł, "Noncommutative tetrads and quantum spacetimes", arXiv:1602.01292.
  13. T. Jurić, A. Samsarov, "Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry", arXiv:1602.01488.
  14. C. P. Martin, J. Trampetić, J. You, "Quantum duality under the θ-exact Seiberg-Witten map", JHEP 1609 (2016) 052
  15. S. Meljanac, D. Meljanac, F. Mercati, D. Pikutić, "Noncommutative spaces and Poincaré symmetry", Phys.Lett. B 766 (2017) 181-185
  16. S. Meljanac, Z. Škoda, M. Stojić, "Lie algebra type noncommutative phase spaces are Hopf algebroids", Lett.Math.Phys. 107 (2017) no.3, 475-503
  17. N. Bilić, D. D. Dimitrijević, G. S. Đorđević, M. Milošević, "Tachyon inflation in an AdS braneworld with backreaction", Int.J.Mod.Phys. A 32 (2017) no.05, 1750039
  18. S. Meljanac, D. Meljanac, S. Mignemi, R. Štrajn, "Quantum field theory in generalised Snyder spaces", Phys.Lett. B 768 (2017) 321-325
  19. S. Mignemi, A. Samsarov, "Relative-locality effects in Snyder spacetime", Phys.Lett. A 381 (2017) 1655-1658
  20. S. Meljanac, D. Meljanac, A. Pachoł, D. Pikutić, "Remarks on simple interpolation between Jordanian twists", J.Phys. A 50 (2017) no.26, 265201
  21. R. Horvat, J. Trampetić, J. You, "Spacetime deformation effect on the early universe and the PTOLEMY experiment", Phys.Lett. B 772 (2017) 130-135
  22. S. Meljanac, S. Krešić-Jurić, T. Martinić, "Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces", J. Math. Phys. 58 (2017) 071701
  23. N. Loret, S. Meljanac, F. Mercati, D. Pikutić, "Vectorlike deformations of relativistic quantum phase-space and relativistic kinematics", Int.J.Mod.Phys. D 26 (2017) no.11, 1750123
  24. K. S. Gupta, T. Jurić, A. Samsarov, "Noncommutative duality and fermionic quasinormal modes of the BTZ black hole", JHEP 1706 (2017) 107
  25. N. Bilić, S. Domazet, G. S. Đorđević, "Tachyon with an inverse power-law potential in a braneworld cosmology", Class.Quant.Grav. 34 (2017) no.16, 165006
  26. T. Jurić, T. Poulain, J.-C. Wallet, "Involutive representations of coordinate algebras and quantum spaces", JHEP 1707 (2017) 116
  27. S. Meljanac, S. Mignemi, J. Trampetić, J. You, "Nonassociative Snyder ϕ4 quantum field theory", Phys.Rev. D 96 (2017) no.4, 045021
  28. N. Bilić, S. Domazet, G. S. Đorđević, "Particle creation and reheating in a braneworld inflationary scenario", Phys.Rev. D 96 (2017) no.8, 083518
  29. S. Meljanac, D. Meljanac, S. Mignemi, R. Štrajn, "Snyder-type space–times, twisted Poincaré algebra and addition of momenta", Int.J.Mod.Phys. A 32 (2017) no.28n29, 1750172
  30. D. Meljanac, S. Meljanac, D. Pikutić, K. S. Gupta, "Twisted statistics and the structure of Lie-deformed Minkowski spaces", Phys.Rev. D 96 (2017) no.10, 105008
  31. D. Meljanac, S. Meljanac, D. Pikutić, "Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries", Eur. Phys. J. C 77 (2017) 830
  32. J. Lukierski, D. Meljanac, S. Meljanac, D. Pikutić, M. Woronowicz, "Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach", Phys.Lett. B 777 (2018) 1–7
  33. Z. Škoda, S. Meljanac, "Hopf algebroid twists for deformation quantization of linear Poisson structures", arXiv:1605.01376.
  34. R. Horvat, C. P. Martin, J. Trampetić, J. You, "Equivalence and/or quantum duality of the non/supersymmetric noncommutative field theories related by the theta-exact Seiberg-Witten map", arXiv:1609.08065.
  35. M. Dimitrijević Ćirić, N. Konjik, A. Samsarov, "Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole", arXiv:1708.04066.
  36. S. Meljanac, S. Krešić-Jurić, D. Pikutić, "Generalization of Weyl realization to a class of Lie superalgebras", arXiv:1710.07494.
  37. D. Meljanac, S. Meljanac, S. Mignemi, D. Pikutić, R. Štrajn, "Twist for Snyder space" , arXiv:1711.02941.
  38. S. Meljanac, S. Mignemi, J. Trampetić, J. You, "UV/IR Mixing in Nonassociative Snyder phi^4 Theory", arXiv:1711.09639.
  39. R. Horvat, J. Trampetić, J. You, "Inferring type and scale of noncommutativity from the PTOLEMY experiment", arXiv:1711.09643.
  40. C. P. Martin, J. Trampetić, J. You, "Quantum noncommutative ABJM theory: first steps", arXiv:1711.09664.
  41. A. Samsarov, "Could LIV/noncommutativity alleviate the cosmological constant problem", arXiv:1711.10894.

External colaborators


Job openings

A call for a position of research associate is open.
Call description:
Research in theoretical and mathematical physics, in particular on quantum gravity and quantum field theory with the emphasis on the use of methods of noncommutative geometry and quantum symmetry.

The deadline is until March 3. For all informations please contact

There will be a call for a postdoc position within the project. It will be announced in September/October 2016. The position is for 6 months and it starts on March 1, 2017. For more information contact

Activities within the HRZZ-project and other activities of the Group for Theoretical and Mathematical physics (conferences, talks, visits)

September 2015:
October 2015:
November 2015:
December 2015:
February 2016:
March 2016:
April 2016:
March 2017:
April 2017:
May 2017:
July 2017:
September 2017:
October 2017:

Contact info

Stjepan Meljanac
senior scientist, Head of Theoretical and mathematical physics group
Phone: +385 1 456 1121