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

**Team Members and Research Group:**- Velimir Bardek, Dr.sc. - senior research associate, RBI
- Nevenko Bilić, Dr. sc. - senior scientist, RBI (retired)
- Silvije Domazet, Dr.sc. - postdoc, RBI
- Raul Horvat, Dr.sc. - senior scientist, RBI
- Tajron Jurić, Dr.sc. - postdoc, RBI
- Danijel Pikutić, Mag.Phys. - PhD student, RBI
- Anđelo Samsarov, Dr.sc. - research associate, RBI
- Rina Štrajn, Dr.sc. - postdoc, RBI (employed by the project)
- Josip Trampetić, Dr. sc. - senior scientist, RBI (retired)
- Jiangyang You, PhD. - postdoc, RBI (employed by the project)

**Starting date:** 1.09.2015.

**Ending date:** 31.8.2017.

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.

- NC differential geometry on deformed spaces
- NC metric
- NC fields in BTZ background
- NC gravity
- NC physics and near horizon geometries
- θ-exact covariant NCQFT
- New couplings/new processes
- Limit on the non-commutative scale
- Application to Astroparticle physics
- Hadronic fluid and AdS/CFT
- K-essence unification and De Sitter invariant propagators

**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.**R. Horvat**,*"Avoiding Boltzmann Brain domination in holographic dark energy models"*, Phys.Lett. B**750**, 181 (2015), arXiv:1502.06348.**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.**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.**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.- 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. **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.**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.**S. Meljanac**, S. Krešić-Jurić and T. Martinić,*"The Weyl realizations of Lie algebras and left-right duality*, arXiv:1511.03936 [math-ph].**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].**N. Bilić**,*"Randall-Sundrum versus holographic cosmology"*, Phys. Rev. D**93**, no. 6, 066010 (2016), arXiv:1511.07323.- A. Borowiec,
**T. Juric**,**S. Meljanac**, A. Pachoł,*"Noncommutative tetrads and quantum spacetimes"*, arXiv:1602.01292. **T. Jurić**,**A. Samsarov**,*"Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry"*, arXiv:1602.01488.- C. P. Martin,
**J. Trampetić**,**J. You**,*"Quantum duality under the θ-exact Seiberg-Witten map"*, JHEP**1609**(2016) 052 **S. Meljanac**, D. Meljanac, F. Mercati,**D. Pikutić**,*"Noncommutative spaces and Poincaré symmetry"*, Phys.Lett. B**766**(2017) 181-185**S. Meljanac**, Z. Škoda, M. Stojić,*"Lie algebra type noncommutative phase spaces are Hopf algebroids"*, Lett.Math.Phys.**107**(2017) no.3, 475-503**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**S. Meljanac**, D. Meljanac, S. Mignemi,**R. Štrajn**,*"Quantum field theory in generalised Snyder spaces"*, Phys.Lett. B**768**(2017) 321-325- S. Mignemi,
**A. Samsarov**,*"Relative-locality effects in Snyder spacetime"*, Phys.Lett. A**381**(2017) 1655-1658 **S. Meljanac**, D. Meljanac, A. Pachoł,**D. Pikutić**,*"Remarks on simple interpolation between Jordanian twists"*, J.Phys. A**50**(2017) no.26, 265201**R. Horvat**,**J. Trampetić**,**J. You**,*"Spacetime deformation effect on the early universe and the PTOLEMY experiment"*, Phys.Lett. B**772**(2017) 130-135**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- 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 - K. S. Gupta,
**T. Jurić**,**A. Samsarov**,*"Noncommutative duality and fermionic quasinormal modes of the BTZ black hole"*, JHEP**1706**(2017) 107 **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**T. Jurić**, T. Poulain, J.-C. Wallet,*"Involutive representations of coordinate algebras and quantum spaces"*, JHEP**1707**(2017) 116**S. Meljanac**, S. Mignemi,**J. Trampetić**,**J. You**,*"Nonassociative Snyder ϕ4 quantum field theory"*, Phys.Rev. D**96**(2017) no.4, 045021**N. Bilić**,**S. Domazet**, G. S. Đorđević,*"Particle creation and reheating in a braneworld inflationary scenario"*, Phys.Rev. D**96**(2017) no.8, 083518**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- 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 - 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 - 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 - Z. Škoda,
**S. Meljanac**,*"Hopf algebroid twists for deformation quantization of linear Poisson structures"*, arXiv:1605.01376. **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.- M. Dimitrijević Ćirić, N. Konjik,
**A. Samsarov**,*"Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole"*, arXiv:1708.04066. **S. Meljanac**, S. Krešić-Jurić,**D. Pikutić**,*"Generalization of Weyl realization to a class of Lie superalgebras"*, arXiv:1710.07494.- D. Meljanac,
**S. Meljanac**, S. Mignemi,**D. Pikutić**,**R. Štrajn**,*"Twist for Snyder space"*, arXiv:1711.02941. **S. Meljanac**, S. Mignemi,**J. Trampetić**,**J. You**,*"UV/IR Mixing in Nonassociative Snyder phi^4 Theory"*, arXiv:1711.09639.**R. Horvat**,**J. Trampetić**,**J. You**,*"Inferring type and scale of noncommutativity from the PTOLEMY experiment"*, arXiv:1711.09643.- C. P. Martin,
**J. Trampetić**,**J. You**,*"Quantum noncommutative ABJM theory: first steps"*, arXiv:1711.09664. **A. Samsarov**,*"Could LIV/noncommutativity alleviate the cosmological constant problem"*, arXiv:1711.10894.

- Saša Krešić-Jurić (University of Split)
- Z. Škoda (PMF, University of Zagreb)
- B. Guberina (RBI, Zagreb)
- Kumar S. Gupta (Theory Division, Saha Institute of Nuclear Physics, Kolkata, India)
- E. Harikumar (School of Physics, University of Hyderabad, Hyderabad, India)
- A. Pachol (Dipartimento di Matematica "Giuseppe Peano",Universita degli Studi di Torino)
- J.C. Wallet (LPT, Orsay, France)
- A. Quiroz (Instituto de Fisica, Universidade de Brasilia)
- A. Borowiec (Institute for Theoretical Physics, University of Wrocław, Wroclaw, Poland)
- S. Mignemi and R. Štrajn (Dipartimento di Matematica e Informatica, Universita di Cagliari, Cagliari, Italy)
- F. Toppan (CBPF, Rio de Janeiro, Brazil)
- B. Jurco (Mathematical Institute Prague, Czech Republic)
- J. Feinberg (University of Haifa, Israel)
- T. Prokopec (Utrecht University, Netherlands)
- G.B. Tupper (University of Cape Town, South Africa)
- I. Shapiro (University of Juiz de Fora, Brazil)
- N. Lorett (RBI, Zagreb)
- Goran Đorđević (University of Niš, Srbija)

- Groups - PhD course, S. Meljanac
- Mathematical methods in physics 1&2 - graduate course, T. Jurić
- Electrodynamics – graduate course, D. Pikutić
- Supersymmetry – graduate course, J. You

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 meljanac@irb.hr

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 meljanac@irb.hr

- dr.sc. S. Meljanac visited prof.dr.sc. S. Krešić-Jurić in University of Split
- dr.sc. T. Jurić and dr.sc. J. You attended Corfu Summer Institute: “Humboldt Kolleg Open Problems in Theoretical Physics: the Issue of Quantum Space-Time” September 18 - 22, 2015 and “Workshop on Noncommutative Field Theory and Gravity” September 21 - 27, 2015
- dr.sc. J. You gave a talk entitled "Tadpole contribution to the noncommutative photon self-energy" within the “Workshop on Noncommutative Field Theory and Gravity”.

October 2015:

- dr.sc. S. Meljanac visited prof.dr.sc. S. Krešić-Jurić in University of Split
- dr.sc. S. Domazet visited prof. T. Prokopec in University of Utrecht
- dr.sc. J. You visited UCM, Madrid, Spain. Topic: Non-commutative field theory
- S. van Tongeren: “ Integrability in string theory and AdS/CFT”, seminar at RBI
- Group for Theoretical and Mathematical Physics (organizer: S. Meljanac) organized the "Symposium Vladimir J. Glaser" with three lectures:
- N. Bilić: “Introductory word about V. Glaser”
- P. Blanchard: “Selected pieces of V. Glaser's typical publications”
- J. Gracia-Bondia: A case study in Epstein-Glaser renormalization

November 2015:

- dr.sc. T. Jurić visited Laboratoire de Physique Theorique d'Orsay, Host: Prof. J. C. Wallet
- dr.sc. J. You visited Max Planck Institute, in Munich, Germany. Topic: Gauge/gravity duality
- Danijel Pikutić attended Bucharest PhD Training School: "Modern Aspects of Quantum Field Theory and Applications", November 8 - 14, 2015
- dr.sc. N Bilić gave a talk entitled "Randall-Sundrum vs. holographic cosmology" within the "11th Vienna Central European Seminar on Particle Physics and Quantum Field Theory", Vienna, 27-29 November 2015.

December 2015:

- prof. Kumar S. Gupta visited RBI. Topics: aspects of noncommutative geometry and black hole physics
- dr. A. Pachol visited RBI. Topic: NC metric
- dr. C. Martin visited RBI. Topic: NC field theory

February 2016:

- On February 1 started the Horizon 2020 project entitled RBI-T-WINNING.
- Members of the Group for Theoretical and Mathematical Physics attended the Kick-off meeting and series of lectures. The lecture in mathematical physics was given by prof. Jean-Christophe Wallet: "Noncommutative gauge theories on quantum spaces: Finiteness, integrability, causal structures"
- D. Pikutić attended the workshop in Zakopane "Quantum spacetime", February 6-12, 2016.
- dr.sc. T. Jurić visited the Theoretical physics department at University of Zaragoza (February 14-20). Host: prof A. Queiroz. Topics: quantum field theory, noncomutative geometry and entanglement entropy
- dr. F. Mercati visited RBI and gave two seminars: "Through the big bang" and "Making noncommutative field theory Lorentz covariant"

March 2016:

- N. Bilić and S. Domazet attended "Rencontres de Moriond: Cosmology 2016", La Thuile, Italy, 19-26 March 2016
- N. Bilić had a poster entitled "Randall-Sundrum vs holographic cosmology"

- Professor Goran Đorđević visited RBI in March 6-9, 2016 for collaboration on topic "Tacyon inflation in and AdS braneworld with backreaction". Collaboration: N. Bilić, S. Domazet (Zagreb), G. Đorđević, D. Dimitrijević, M. Milošević (Niš)
- dr.sc. T. Jurić visited the Laboratoire de Physique Theorique d'Orsay (March 1-30). Host: Prof. J. C. Wallet. Topics: quantum field theory, noncomutative geometry and spectral triples

April 2016:

- dr.sc. T. Jurić visited SISSA, Trieste (April 17-24). Host: Prof. L. Dabrowski. Topics: quantum field theory, noncomutative geometry and spectral triples. He give a talk entitled "Some examples of NCQFT and NC metric"

March 2017:

- dr.sc. T. Jurić gave a talk entitled "Effects of Noncommutativity on the Black Hole Entropy and QNM" within the "Topological and geometrical aspects of quantum spaces: field theory and causal structure", Trieste, 13-17 March 2017

April 2017:

- dr.sc. N. Bilić gave a talk entitled "Braneworld cosmology and holography" within the "Progress on Old and New Themes in cosmology (PONT) 2017", Avignon, 24-28 April 2017

May 2017:

- dr.sc. T. Jurić gave a talk entitled "Noncommutative Geometry and Physics" at the University of Brasilia, 11 May 2017
- dr.sc. A. Samsarov gave a talk entitled "Black hole quasinormal modes in twisted models of matter minimally coupled to gravity" at the University of Vienna, 30 May 2017

July 2017:

- dr.sc. N. Bilić gave a talk entitled "Emergent Spacetime in the Laboratory" within the "The Sixth PHYSICS & PHILOSOPHY Meeting in Conjunction with the Summer School", Split, 4-6 July 2017
- dr.sc. N. Bilić gave a talk entitled "Space and Time in Modern Cosmology" within the "The Sixth PHYSICS & PHILOSOPHY Meeting in Conjunction with the Summer School", Split, 4-6 July 2017

September 2017:

- dr.sc. R. Štrajn gave a talk entitled "Snyder-type spacetimes, twisted Poincare algebra and addition of momenta" within the training school "Quantum Spacetime and Physics Models", Corfu, 16-23 September 2017
- dr.sc. N. Bilić gave a talk entitled "Aspects of braneworld cosmology and holography" within the "9th MATHEMATICAL PHYSICS MEETING: School and Conference on Modern Mathematical Physics", Belgrade, 18-23 September 2017

October 2017:

- dr.sc. R. Štrajn gave a talk entitled "Prostori Snyderovog tipa, zakretanje Poincareove algebre i zbrajanje impulsa" within the 10. znanstveni sastanak HFD-a, Baška, 11-13 October 2017

Stjepan Meljanac

senior scientist, Head of Theoretical and mathematical physics group

Email: meljanac@irb.hr

Phone: +385 1 456 1121