The Snyder Model and Quantum Field Theory

Authors

  • S. Mignemi Dipartimento di Matematica e Informatica, Universit´a di Cagliari, INFN, Sezione di Cagliari

DOI:

https://doi.org/10.15407/ujpe64.11.991

Keywords:

Snyder model, noncommutative field theory

Abstract

We review the main features of the relativistic Snyder model and its generalizations. We discuss the quantum field theory on this background using the standard formalism of noncommutative QFT and discuss the possibility of obtaining a finite theory.

References

L.J. Garay. Quantum gravity and minimum length. Int. J. Mod. Phys. A 10, 145 (1995). https://doi.org/10.1142/S0217751X95000085

S. Hossenfelder. Minimal length scale scenarios for quantum gravity. Liv. Rev. Rel. 16, 2 (2013). https://doi.org/10.12942/lrr-2013-2

H.S. Snyder. Quantized space-time. Phys. Rev. 71, 38 (1947). https://doi.org/10.1103/PhysRev.71.38

H.S. Snyder. The electromagnetic field in quantized spacetime. Phys. Rev. 72, 68 (1947). https://doi.org/10.1103/PhysRev.72.68

A. Connes. Noncommutative Geometry (Academic Press, 1994).

J. Madore. An Introduction to Noncommutative Differential Geometry and Its Physical Applications (Cambridge Univ. Press, 1999). https://doi.org/10.1017/CBO9780511569357

M.R. Douglas, N.A. Nekrasov. Noncommutative field theory. Rev. Mod. Phys. 73, 977 (2001). https://doi.org/10.1103/RevModPhys.73.977

R.J. Szabo. Quantum field theory on noncommutative spaces. Phys. Rept. 378, 207 (2003). https://doi.org/10.1016/S0370-1573(03)00059-0

S. Majid. Foundations of Quantum Group Theory (Cambridge Univ. Press, 1995). https://doi.org/10.1017/CBO9780511613104

G. Amelino-Camelia. Relativity in spacetimes with short-distance structure governed by an observer-independent (Planckian) length scale. Int. J. Mod. Phys. D 11, 35 (2002). https://doi.org/10.1142/S0218271802001330

G. Amelino-Camelia. Testable scenario for relativity with minimum length. Phys. Lett. B 510, 255 (2001). https://doi.org/10.1016/S0370-2693(01)00506-8

J. Kowalski-Glikman. De Sitter space as an arena for doubly special relativity. Phys. Lett. B 547, 291 (2002). https://doi.org/10.1016/S0370-2693(02)02762-4

J. Kowalski-Glikman, S. Nowak. Doubly special relativity and de Sitter space. Class. Quantum Grav. 20, 4799 (2003). https://doi.org/10.1088/0264-9381/20/22/006

Y.A. Gol'fand. Quantum field theory in constant curvature p-space. Sov. Phys. JETP 16, 184 (1963).

Y.A. Gol'fand. On the properties of displacements in p-space of constant curvature. Sov. Phys. JETP 17, 842 (1963).

Y.A. Gol'fand. On the introduction of an "elementary length" in the relativistic theory of elementary particles. Sov. Phys. JETP 37, 356 (1960).

V.G. Kadyshevsky. On the theory of quantization of spacetime. Sov. Phys. JETP 14, 1340 (1962).

R.M. Mir-Kasimov. "Focusing" singularity in p-space of constant curvature. Sov. Phys. JETP 22, 629 (1966).

R.M. Mir-Kasimov. The Coulomb field and the nonrelativistic quantization of space. Sov. Phys. JETP 25, 348 (1967).

J.C. Breckenridge, T.G. Steele, V. Elias. Massless scalar field theory in a quantized space-time. Class. Quantum Grav. 12, 637 (1995). https://doi.org/10.1088/0264-9381/12/3/004

T. Konopka. A field theory model with a new Lorentz-invariant energy scale. Mod. Phys. Lett. A 23, 319 (2008). https://doi.org/10.1142/S0217732308026443

S. Meljanac, S. Mignemi, J. Trampeti?c, J. You. Nonassociative Snyder ф4 quantum field theory. Phys. Rev. D 96, 045021 (2017). https://doi.org/10.1103/PhysRevD.96.045021

A. Franchino-Vi?nas, S. Mignemi. Worldline formalism in Snyder spaces. Phys. Rev. D 98, 065010 (2018). https://doi.org/10.1103/PhysRevD.98.065010

S. Meljanac, S. Mignemi, J. Trampeti?c, J. You. UV-IR mixing in nonassociative Snyder ф4 theory. Phys. Rev. D 97, 055041 (2018).https://doi.org/10.1103/PhysRevD.97.055041

M.V. Battisti, S. Meljanac. Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry. Phys. Rev. D 79, 067505 (2009). https://doi.org/10.1103/PhysRevD.79.067505

M.V. Battisti, S. Meljanac. Scalar field theory on noncommutative Snyder spacetime. Phys. Rev. D 82, 024028 (2010). https://doi.org/10.1103/PhysRevD.82.024028

B. Iveti?c, S. Mignemi. Relative-locality geometry for the Snyder model. Int. J. Mod. Phys. D 27, 1950010 (2018). https://doi.org/10.1142/S021827181950010X

S. Meljanac, D. Meljanac, S. Mignemi, R. ? Strajn. Quantum field theory in generalised Snyder spaces. Phys. Lett. B 768, 321 (2017). https://doi.org/10.1016/j.physletb.2017.02.059

C.N. Yang. On quantized space-time. Phys. Rev. 72, 874 (1947). https://doi.org/10.1103/PhysRev.72.874

J. Kowalski-Glikman, L. Smolin. Triply special relativity. Phys. Rev. D 70, 065020 (2004). https://doi.org/10.1103/PhysRevD.70.065020

H.G. Guo, C.G. Huang, H.T. Wu. Yang's model as triply special relativity and the Snyder's model-de Sitter special relativity duality. Phys. Lett. B 663, 270-274 (2008). https://doi.org/10.1016/j.physletb.2008.04.012

M. Born. Reciprocity theory of elementary particles. Rev. Mod. Phys. 21, 463 (1949). https://doi.org/10.1103/RevModPhys.21.463

S. Mignemi. The Snyder-de Sitter model from six dimensions. Class. Quantum Grav. 26, 245020 (2009). https://doi.org/10.1088/0264-9381/26/24/245020

G. Veneziano. A stringy nature needs just two constants. Europhys. Lett. 2, 199 (1986). https://doi.org/10.1209/0295-5075/2/3/006

M. Maggiore. A generalized uncertainty principle in quantum gravity. Phys. Lett. B 304, 65 (1993). https://doi.org/10.1016/0370-2693(93)91401-8

S. Mignemi, R. ? Strajn. Snyder dynamics in a Schwarzschild spacetime. Phys. Rev. D 90, 044019 (2014). https://doi.org/10.1103/PhysRevD.90.044019

S. Mignemi, A. Samsarov. Relative-locality effects in Snyder spacetime. Phys. Lett. A 381, 1655 (2017). https://doi.org/10.1016/j.physleta.2017.03.033

S. Mignemi, G. Rosati. Relative-locality phenomenology on Snyder spacetime. Class. Quantum Grav. 35, 145006 (2018). https://doi.org/10.1088/1361-6382/aac9d5

G. Gubitosi, F. Mercati. Relative locality in к-Poincar?e. Class. Quantum Grav. 20, 145002 (2013). https://doi.org/10.1088/0264-9381/30/14/145002

F. Girelli, E. Livine. Scalar field theory in Snyder spacetime: alternatives. JHEP 1103, 132 (2011). https://doi.org/10.1007/JHEP03(2011)132

S. Meljanac, Z. ? Skoda, D. Svrtan. Exponential formulas and Lie algebra type star products. SIGMA 8, 013 (2012). https://doi.org/10.3842/SIGMA.2012.013

H. Grosse, R. Wulkenhaar. Renormalisation of Renormalisation of 4-theory on noncommutative R4 in the matrix base. Commun. Math. Phys. 256, 305 (2005). https://doi.org/10.1007/s00220-004-1285-2

A. Franchino-Vi?nas, S. Mignemi, in preparation.

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Published

2019-11-25

How to Cite

Mignemi, S. (2019). The Snyder Model and Quantum Field Theory. Ukrainian Journal of Physics, 64(11), 991. https://doi.org/10.15407/ujpe64.11.991

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Section

Fields and elementary particles