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SIGMA, 2010, Volume 6, 052, 22 pages (Mi sigma509)  

This article is cited in 22 scientific papers (total in 22 papers)

Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology

Aiyalam P. Balachandrana, Alberto Ibortb, Giuseppe Marmocd, Mario Martonecad

a Department of Physics, Syracuse University, Syracuse, NY 13244-1130, USA
b Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain
c INFN, Via Cinthia I-80126 Napoli, Italy
d Dipartimento di Scienze Fisiche, University of Napoli

Abstract: In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincaré invariance. We present the latest development in the field, in particular the notion of equivalence of such quantum field theories on a noncommutative spacetime, in this regard we work out explicitly the inequivalence between twisted quantum field theories on Moyal and Wick–Voros planes; the duality between deformations of the multiplication map on the algebra of functions on spacetime $\mathscr F(\mathbb R^4)$ and coproduct deformations of the Poincaré–Hopf algebra $H\mathscr P$ acting on $\mathscr F(\mathbb R^4)$; the appearance of a nonassociative product on $\mathscr F(\mathbb{R}^4)$ when gauge fields are also included in the picture. The last part of the manuscript is dedicated to the phenomenology of noncommutative quantum field theories in the particular approach adopted in this review. CPT violating processes, modification of two-point temperature correlation function in CMB spectrum analysis and Pauli-forbidden transition in $\mathrm Be^4$ are all effects which show up in such a noncommutative setting. We review how they appear and in particular the constraint we can infer from comparison between theoretical computations and experimental bounds on such effects. The best bound we can get, coming from Borexino experiment, is $\gtrsim10^{24}$ TeV for the energy scale of noncommutativity, which corresponds to a length scale $\lesssim 10^{-43}$ m. This bound comes from a different model of spacetime deformation more adapted to applications in atomic physics. It is thus model dependent even though similar bounds are expected for the Moyal spacetime as well as argued elsewhere.

Keywords: noncommutative spacetime; quantum field theory; twisted field construction; Poincaré–Hopf algebra

DOI: https://doi.org/10.3842/SIGMA.2010.052

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ArXiv: 1003.4356
MSC: 81R50; 81R60
Received: March 24, 2010; in final form June 8, 2010; Published online June 21, 2010
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Citation: Aiyalam P. Balachandran, Alberto Ibort, Giuseppe Marmo, Mario Martone, “Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology”, SIGMA, 6 (2010), 052, 22 pp.

Citation in format AMSBIB
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\by Aiyalam P.~Balachandran, Alberto Ibort, Giuseppe Marmo, Mario Martone
\paper Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
\jour SIGMA
\yr 2010
\vol 6
\papernumber 052
\totalpages 22
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\crossref{https://doi.org/10.3842/SIGMA.2010.052}
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    This publication is cited in the following articles:
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    2. Gromov N.A., “Possible quantum kinematics. II. Nonminimal case”, J. Math. Phys., 51:8 (2010), 083515, 12 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Balachandran A.P., Joseph A., Padmanabhan P., “Non-Pauli Transitions from Spacetime Noncommutativity”, Phys. Rev. Lett., 105:5 (2010), 051601, 4 pp.  crossref  mathscinet  adsnasa  isi  elib  scopus
    4. Haghighat M., Okada N., Stern A., “Location and direction dependent effects in collider physics from noncommutativity”, Phys. Rev. D, 82:1 (2010), 016007, 6 pp.  crossref  mathscinet  adsnasa  isi  elib  scopus
    5. Balachandran A.P., Ibort A., Marmo G., Martone M., “Covariant quantum fields on noncommutative spacetimes”, Journal of High Energy Physics, 2011, no. 3, 057  crossref  mathscinet  zmath  isi  scopus
    6. Balachandran A.P., Ibort A., Marmo G., Martone M., “Quantum geons and noncommutative spacetimes”, Gen Relativity Gravitation, 43:12 (2011), 3531–3567  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Balachandran A.P., Padmanabhan P., de Queiroz A.R., “Lehmann-Symanzik-Zimmermann S-matrix elements on the Moyal plane”, Phys Rev D, 84:6 (2011), 065020  crossref  adsnasa  isi  elib  scopus
    8. Chandra N., “Time-dependent transitions with time-space noncommutativity and its implications in quantum optics”, Journal of Physics A-Mathematical and Theoretical, 45:1 (2012), 015307  crossref  mathscinet  zmath  adsnasa  isi  scopus
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    10. Dupuis M., Girelli F., Livine E.R., “Spinors Group Field Theory and Voros Star Product: First Contact”, Phys. Rev. D, 86:10 (2012), 105034  crossref  adsnasa  isi  scopus
    11. Devi Y.Ch., Ghosh Kumar Jang Bahadur, Chakraborty B., Scholtz F.G., “Thermal Effective Potential in Two- and Three-Dimensional Non-Commutative Spaces”, J. Phys. A-Math. Theor., 47:2 (2014), 025302  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Santos W.O., Souza A.M.C., “Phenomenology of Noncommutative Phase Space Via the Anomalous Zeeman Effect in Hydrogen Atom”, Int. J. Mod. Phys. A, 29:31 (2014), 1450177  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Calcagni G., “Multifractional theories: an unconventional review”, J. High Energy Phys., 2017, no. 3, 138  crossref  mathscinet  zmath  isi  scopus
    14. Amelino-Camelia G., Calcagni G., Ronco M., “Imprint of Quantum Gravity in the Dimension and Fabric of Spacetime”, Phys. Lett. B, 774 (2017), 630–634  crossref  isi  scopus
    15. Gnatenko Kh.P., Tkachuk V.M., “Noncommutative Phase Space With Rotational Symmetry and Hydrogen Atom”, Int. J. Mod. Phys. A, 32:26 (2017), 1750161  crossref  mathscinet  zmath  isi
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    18. Calcagni G., “Cosmology of Quantum Gravities”: G. Calcagni, Classical and Quantum Cosmology, Graduate Texts in Physics, Springer International Publishing Ag, 2017, 543–624  crossref  mathscinet  isi
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  • Symmetry, Integrability and Geometry: Methods and Applications
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