Geodesic
Realizations of the Extended Snyder Model
Symmetry, integrability and geometry: methods and applications, Tome 19 (2023) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We present the exact realization of the extended Snyder model. Using similarity transformations, we construct realizations of the original Snyder and the extended Snyder models. Finally, we present the exact new realization of the $\kappa$-deformed extended Snyder model.
Keywords: Snyder model, extended Snyder model, $\kappa$-deformed extended Snyder model, realizations. 
@article{SIGMA_2023_19_a64,
     author = {Tea Martini\'c Bila\'c and Stjepan Meljanac},
     title = {Realizations of the {Extended} {Snyder} {Model}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2023},
     volume = {19},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a64/}
}
TY  - JOUR
AU  - Tea Martinić Bilać
AU  - Stjepan Meljanac
TI  - Realizations of the Extended Snyder Model
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2023
VL  - 19
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a64/
LA  - en
ID  - SIGMA_2023_19_a64
ER  - 
%0 Journal Article
%A Tea Martinić Bilać
%A Stjepan Meljanac
%T Realizations of the Extended Snyder Model
%J Symmetry, integrability and geometry: methods and applications
%D 2023
%V 19
%U http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a64/
%G en
%F SIGMA_2023_19_a64
Tea Martinić Bilać; Stjepan Meljanac. Realizations of the Extended Snyder Model. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a64/

[1] Amelino-Camelia G., Arzano M., “Coproduct and star product in field theories on Lie-algebra noncommutative space-times”, Phys. Rev. D, 65 (2002), 084044, 8 pp., arXiv: hep-th/0105120 | DOI | MR

[2] Amelino-Camelia G., Lukierski J., Nowicki A., “$\kappa$-deformed covariant phase space and quantum-gravity uncertainty relations”, Phys. Atomic Nuclei, 61 (1998), 1811–1815, arXiv: hep-th/9706031 | MR

[3] Arzano M., Kowalski-Glikman J., “Deformations of spacetime symmetries – gravity, group-valued momenta, and non-commutative fields”, Lecture Notes in Phys., 986, Springer, Berlin, 2021 | DOI | MR | Zbl

[4] Banerjee R., Kumar K., Roychowdhury D., “Symmetries of Snyder–de Sitter space and relativistic particle dynamics”, J. High Energy Phys., 2011:3 (2011), 060, 14 pp., arXiv: 1101.2021 | DOI | MR | Zbl

[5] Battisti M.V., Meljanac S., “Modification of Heisenberg uncertainty relations in noncommutative Snyder space-time geometry”, Phys. Rev. D, 79 (2009), 067505, 4 pp., arXiv: 0812.3755 | DOI | MR

[6] Battisti M.V., Meljanac S., “Scalar field theory on noncommutative Snyder spacetime”, Phys. Rev. D, 82 (2010), 024028, 9 pp., arXiv: 1003.2108 | DOI | MR

[7] Borowiec A., Pachoł A., “The classical basis for the $\kappa$-Poincaré Hopf algebra and doubly special relativity theories”, J. Phys. A, 43 (2010), 045203, 10 pp., arXiv: 0903.5251 | DOI | MR | Zbl

[8] Doplicher S., Fredenhagen K., Roberts J.E., “Spacetime quantization induced by classical gravity”, Phys. Lett. B, 331 (1994), 39–44 | DOI | MR

[9] Doplicher S., Fredenhagen K., Roberts J.E., “The quantum structure of spacetime at the Planck scale and quantum fields”, Comm. Math. Phys., 172 (1995), 187–220, arXiv: hep-th/0303037 | DOI | MR | Zbl

[10] Franchino-Viñas S.A., Mignemi S., “Worldline formalism in Snyder spaces”, Phys. Rev. D, 98 (2018), 065010, 10 pp., arXiv: 1806.11467 | DOI | MR

[11] Garay L.J., “Quantum gravity and minimum length”, Internat. J. Modern Phys. A, 10 (1995), 145–165, arXiv: gr-qc/9403008 | DOI

[12] Girelli F., Livine E.R., “Scalar field theory in Snyder space-time: alternatives”, J. High Energy Phys., 2011:3 (2011), 132, 31 pp., arXiv: 1004.0621 | DOI | MR | Zbl

[13] Guo H.-Y., Huang C.-G., Wu H.-T., “Yang's model as triply special relativity and the Snyder's model – de Sitter special relativity duality”, Phys. Lett. B, 663 (2008), 270–274, arXiv: 0801.1146 | DOI | MR | Zbl

[14] Kowalski-Glikman J., Nowak S., “Non-commutative space-time of doubly special relativity theories”, Internat. J. Modern Phys. D, 12 (2003), 299–315, arXiv: hep-th/0204245 | DOI | MR | Zbl

[15] Kowalski-Glikman J., Smolin L., “Triply special relativity”, Phys. Rev. D, 70 (2004), 065020, 6 pp., arXiv: hep-th/0406276 | DOI | MR

[16] Lukierski J., Meljanac S., Mignemi S., Pachoł A., Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking, arXiv: 2212.02316

[17] Lukierski J., Meljanac S., Mignemi S., Pachoł A., “Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model”, Phys. Lett. B, 838 (2023), 137709, 8 pp., arXiv: 2208.06712 | DOI | MR

[18] Lukierski J., Nowicki A., Ruegg H., “New quantum Poincaré algebra and $\kappa$-deformed field theory”, Phys. Lett. B, 293 (1992), 344–352 | DOI | MR | Zbl

[19] Lukierski J., Ruegg H., Nowicki A., Tolstoy V.N., “$q$-deformation of Poincaré algebra”, Phys. Lett. B, 264 (1991), 331–338 | DOI | MR

[20] Majid S., Foundations of quantum group theory, Cambridge University Press, Cambridge, 1995 | DOI | MR | Zbl

[21] Meljanac S., Krešić-Jurić S., “Differential structure on $\kappa$-Minkowski space, and $\kappa$-Poincaré algebra”, Internat. J. Modern Phys. A, 26 (2011), 3385–3402, arXiv: 1004.4647 | DOI | MR | Zbl

[22] Meljanac S., Krešić-Jurić S., Stojić M., “Covariant realizations of kappa-deformed space”, Eur. Phys. J. C, 51 (2007), 229–240, arXiv: hep-th/0702215 | DOI | MR | Zbl

[23] Meljanac S., Martinić Bilać T., Krešić-Jurić S., “Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz, and Poincaré algebras and their dual extensions”, J. Math. Phys., 61 (2020), 051705, 13 pp., arXiv: 2003.02726 | DOI | MR | Zbl

[24] Meljanac S., Meljanac D., Samsarov A., Stojić M., “$\kappa$-deformed Snyder spacetime”, Modern Phys. Lett. A, 25 (2010), 579–590, arXiv: 0912.5087 | DOI | MR | Zbl

[25] Meljanac S., Meljanac D., Samsarov A., Stojic M., “Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra”, Phys. Rev. D, 83 (2011), 065009, 16 pp., arXiv: 1102.1655 | DOI

[26] Meljanac S., Mignemi S., “Associative realizations of the extended Snyder model”, Phys. Rev. D, 102 (2020), 126011, 9 pp., arXiv: 2007.13498 | DOI | MR

[27] Meljanac S., Mignemi S., “Associative realizations of $\kappa$-deformed extended Snyder model”, Phys. Rev. D, 104 (2021), 086006, 9 pp., arXiv: 2106.08131 | DOI | MR

[28] Meljanac S., Mignemi S., “Unification of $\kappa$-Minkowski and extended Snyder spaces”, Phys. Lett. B, 814 (2021), 136117, 5 pp., arXiv: 2101.05275 | DOI | MR | Zbl

[29] Meljanac S., Mignemi S., “Generalizations of Snyder model to curved spaces”, Phys. Lett. B, 833 (2022), 137289, 6 pp., arXiv: 2206.04772 | DOI | MR | Zbl

[30] Meljanac S., Mignemi S., “Noncommutative Yang model and its generalizations”, J. Math. Phys., 64 (2023), 023505, 9 pp., arXiv: 2211.11755 | DOI | MR | Zbl

[31] Meljanac S., Pachoł A., “Heisenberg doubles for Snyder-type models”, Symmetry, 13 (2021), 1055, 13 pp., arXiv: 2101.02512 | DOI

[32] Meljanac S., Štrajn R., “Deformed quantum phase spaces, realizations, star products and twists”, SIGMA, 18 (2022), 022, 20 pp., arXiv: 2112.12038 | DOI | MR | Zbl

[33] Mignemi S., “The Snyder–de Sitter model from six dimensions”, Classical Quantum Gravity, 26 (2009), 245020, 9 pp. | DOI | MR | Zbl

[34] Mignemi S., Rosati G., “Relative-locality phenomenology on Snyder spacetime”, Classical Quantum Gravity, 35 (2018), 145006, 17 pp., arXiv: 1803.02134 | DOI | MR | Zbl

[35] Mignemi S., Štrajn R., “Snyder dynamics in a Schwarzschild spacetime”, Phys. Rev. D, 90 (2014), 044019, 5 pp., arXiv: 1404.6396 | DOI

[36] Snyder H.S., “Quantized space-time”, Phys. Rev., 71 (1947), 38–41 | DOI | MR | Zbl