Abstract
We construct a noncommutative kappa-Minkowski deformation of U(1) gauge theory, following a general approach, recently proposed in JHEP 08 (2020) 041. We obtain an exact (all orders in the non-commutativity parameter) expression for both the deformed gauge transformations and the deformed field strength, which is covariant under these transformations. The corresponding Yang-Mills Lagrangian is gauge covariant and reproduces the Maxwell Lagrangian in the commutative limit. Gauge invariance of the action functional requires a non-trivial integration measure which, in the commutative limit, does not reduce to the trivial one. We discuss the physical meaning of such a nontrivial commutative limit, relating it to a nontrivial space-time curvature of the undeformed theory. Moreover, we propose a rescaled kappa-Minkowski noncommutative structure, which exhibits a standard flat commutative limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Blumenhagen, I. Brunner, V. Kupriyanov and D. Lüst, Bootstrapping non-commutative gauge theories from L∞ algebras, JHEP 05 (2018) 097 [arXiv:1803.00732] [INSPIRE].
V.G. Kupriyanov and P. Vitale, A novel approach to non-commutative gauge theory, JHEP 08 (2020) 041 [arXiv:2004.14901] [INSPIRE].
G. Amelino-Camelia and S. Majid, Waves on noncommutative space-time and gamma-ray bursts, Int. J. Mod. Phys. A 15 (2000) 4301 [hep-th/9907110] [INSPIRE].
J. Kowalski-Glikman and S. Nowak, Doubly special relativity theories as different bases of kappa Poincaré algebra, Phys. Lett. B 539 (2002) 126 [hep-th/0203040] [INSPIRE].
J. Lukierski and A. Nowicki, Doubly special relativity versus kappa deformation of relativistic kinematics, Int. J. Mod. Phys. A 18 (2003) 7 [hep-th/0203065] [INSPIRE].
A. Borowiec, K.S. Gupta, S. Meljanac and A. Pachol, Constarints on the quantum gravity scale from κ-Minkowski spacetime, EPL 92 (2010) 20006 [arXiv:0912.3299] [INSPIRE].
G. Gubitosi and F. Mercati, Relative Locality in κ-Poincaré, Class. Quant. Grav. 30 (2013) 145002 [arXiv:1106.5710] [INSPIRE].
P. Aschieri, A. Borowiec and A. Pachoł, Observables and dispersion relations in κ-Minkowski spacetime, JHEP 10 (2017) 152 [arXiv:1703.08726] [INSPIRE].
S. Meljanac, D. Meljanac, F. Mercati and D. Pikutić, Noncommutative spaces and Poincaré symmetry, Phys. Lett. B 766 (2017) 181 [arXiv:1610.06716] [INSPIRE].
F. Lizzi, M. Manfredonia, F. Mercati and T. Poulain, Localization and Reference Frames in κ-Minkowski Spacetime, Phys. Rev. D 99 (2019) 085003 [arXiv:1811.08409] [INSPIRE].
F. Lizzi, M. Manfredonia and F. Mercati, The momentum spaces of κ-Minkowski noncommutative spacetime, Nucl. Phys. B 958 (2020) 115117 [arXiv:2001.08756] [INSPIRE].
J. Madore, S. Schraml, P. Schupp and J. Wess, Gauge theory on noncommutative spaces, Eur. Phys. J. C 16 (2000) 161 [hep-th/0001203] [INSPIRE].
P. Kosiński, J. Lukierski and P. Maślanka, Local D = 4 field theory on kappa deformed Minkowski space, Phys. Rev. D 62 (2000) 025004 [hep-th/9902037] [INSPIRE].
M. Dimitrijević, L. Jonke, L. Möller, E. Tsouchnika, J. Wess and M. Wohlgenannt, Deformed field theory on kappa space-time, Eur. Phys. J. C 31 (2003) 129 [hep-th/0307149] [INSPIRE].
F. Meyer and H. Steinacker, Gauge field theory on the Eq(2) covariant plane, Int. J. Mod. Phys. A 19 (2004) 3349 [hep-th/0309053] [INSPIRE].
M. Dimitrijević, F. Meyer, L. Möller and J. Wess, Gauge theories on the kappa Minkowski space-time, Eur. Phys. J. C 36 (2004) 117 [hep-th/0310116] [INSPIRE].
L. Freidel and E.R. Livine, 3D Quantum Gravity and Effective Noncommutative Quantum Field Theory, Bulg. J. Phys. 33 (2006) 111.
M. Arzano and A. Marciano, Fock space, quantum fields and kappa-Poincaré symmetries, Phys. Rev. D 76 (2007) 125005 [arXiv:0707.1329] [INSPIRE].
T.R. Govindarajan, K.S. Gupta, E. Harikumar, S. Meljanac and D. Meljanac, Twisted statistics in kappa-Minkowski spacetime, Phys. Rev. D 77 (2008) 105010 [arXiv:0802.1576] [INSPIRE].
M. Dimitrijević and L. Jonke, A Twisted look on kappa-Minkowski: U(1) gauge theory, JHEP 12 (2011) 080 [arXiv:1107.3475] [INSPIRE].
J. Lukierski, H. Ruegg, A. Nowicki and V.N. Tolstoi, Q deformation of Poincaré algebra, Phys. Lett. B 264 (1991) 331 [INSPIRE].
A. Sitarz, Noncommutative differential calculus on the kappa Minkowski space, Phys. Lett. B 349 (1995) 42 [hep-th/9409014] [INSPIRE].
A. Agostini, F. Lizzi and A. Zampini, Generalized Weyl systems and kappa Minkowski space, Mod. Phys. Lett. A 17 (2002) 2105 [hep-th/0209174] [INSPIRE].
S. Meljanac, A. Samsarov, M. Stojic and K.S. Gupta, Kappa-Minkowski space-time and the star product realizations, Eur. Phys. J. C 53 (2008) 295 [arXiv:0705.2471] [INSPIRE].
A. Borowiec and A. Pachol, kappa-Minkowski spacetime as the result of Jordanian twist deformation, Phys. Rev. D 79 (2009) 045012 [arXiv:0812.0576] [INSPIRE].
B. Durhuus and A. Sitarz, Star product realizations of kappa-Minkowski space, J. Noncommut. Geom. 7 (2013) 605 [arXiv:1104.0206] [INSPIRE].
A. Pachoł and P. Vitale, κ-Minkowski star product in any dimension from symplectic realization, J. Phys. A 48 (2015) 445202 [arXiv:1507.03523] [INSPIRE].
M. Kontsevich, Deformation quantization of Poisson manifolds. 1., Lett. Math. Phys. 66 (2003) 157 [q-alg/9709040] [INSPIRE].
V.G. Kupriyanov, L∞-Bootstrap Approach to Non-Commutative Gauge Theories, Fortsch. Phys. 67 (2019) 1910010 [arXiv:1903.02867] [INSPIRE].
V.G. Kupriyanov, Non-commutative deformation of Chern-Simons theory, Eur. Phys. J. C 80 (2020) 42 [arXiv:1905.08753] [INSPIRE].
R. Blumenhagen, M. Brinkmann, V. Kupriyanov and M. Traube, On the Uniqueness of L∞ bootstrap: Quasi-isomorphisms are Seiberg-Witten Maps, J. Math. Phys. 59 (2018) 123505 [arXiv:1806.10314] [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
G. Felder and B. Shoikhet, Deformation quantisation with traces, Lett. Math. Phys. 53 (2000) 75 [math.QA/0002057].
S. Gutt and J. Rawnsley, Traces for star products on symplectic manifolds, J. Geom. Phys. 42 (2002) 12.
V.G. Kupriyanov, A hydrogen atom on curved noncommutative space, J. Phys. A 46 (2013) 245303 [arXiv:1209.6105] [INSPIRE].
V.G. Kupriyanov, Quantum mechanics with coordinate dependent noncommutativity, J. Math. Phys. 54 (2013) 112105 [arXiv:1204.4823] [INSPIRE].
P. Mathieu and J.-C. Wallet, Gauge theories on κ-Minkowski spaces: twist and modular operators, JHEP 05 (2020) 112 [arXiv:2002.02309] [INSPIRE].
T. Poulain and J.-C. Wallet, κ-Poincaré invariant orientable field theories at one-loop, JHEP 01 (2019) 064 [arXiv:1808.00350] [INSPIRE].
T. Poulain and J.C. Wallet, κ-Poincaré invariant quantum field theories with KMS weight, Phys. Rev. D 98 (2018) 025002 [arXiv:1801.02715] [INSPIRE].
M. Dimitrijević Ciric, N. Konjik, M.A. Kurkov, F. Lizzi and P. Vitale, Noncommutative field theory from angular twist, Phys. Rev. D 98 (2018) 085011 [arXiv:1806.06678] [INSPIRE].
F. Canfora, M. Kurkov, L. Rosa and P. Vitale, The Gribov problem in Noncommutative QED, JHEP 01 (2016) 014 [arXiv:1505.06342] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2010.09863
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kupriyanov, V.G., Kurkov, M. & Vitale, P. κ-Minkowski-deformation of U(1) gauge theory. J. High Energ. Phys. 2021, 102 (2021). https://doi.org/10.1007/JHEP01(2021)102
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2021)102