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Title: Noncommutative spaces, the quantum of time, and Lorentz symmetry

Abstract

We introduce three space-times that are discrete in time and compatible with the Lorentz symmetry. We show that these spaces are not commutative, with commutation relations similar to the relations of the Snyder and Yang spaces. Furthermore, using a reparametrized relativistic particle we obtain a realization of the Snyder type spaces and we construct an action for them.

Authors:
; ;  [1];  [2]
  1. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico 04510 DF (Mexico)
  2. (Mexico)
Publication Date:
OSTI Identifier:
21020187
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.065008; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; COMMUTATION RELATIONS; LORENTZ INVARIANCE; QUANTUM FIELD THEORY; RELATIVISTIC RANGE; SPACE; SPACE-TIME; SYMMETRY

Citation Formats

Romero, Juan M., Vergara, J. D., Santiago, J. A., and Centro de Investigacion Avanzada en Ingenieria Industrial, Universidad Autonoma del Estado de Hidalgo, Pachuca 42090. Noncommutative spaces, the quantum of time, and Lorentz symmetry. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.065008.
Romero, Juan M., Vergara, J. D., Santiago, J. A., & Centro de Investigacion Avanzada en Ingenieria Industrial, Universidad Autonoma del Estado de Hidalgo, Pachuca 42090. Noncommutative spaces, the quantum of time, and Lorentz symmetry. United States. doi:10.1103/PHYSREVD.75.065008.
Romero, Juan M., Vergara, J. D., Santiago, J. A., and Centro de Investigacion Avanzada en Ingenieria Industrial, Universidad Autonoma del Estado de Hidalgo, Pachuca 42090. Thu . "Noncommutative spaces, the quantum of time, and Lorentz symmetry". United States. doi:10.1103/PHYSREVD.75.065008.
@article{osti_21020187,
title = {Noncommutative spaces, the quantum of time, and Lorentz symmetry},
author = {Romero, Juan M. and Vergara, J. D. and Santiago, J. A. and Centro de Investigacion Avanzada en Ingenieria Industrial, Universidad Autonoma del Estado de Hidalgo, Pachuca 42090},
abstractNote = {We introduce three space-times that are discrete in time and compatible with the Lorentz symmetry. We show that these spaces are not commutative, with commutation relations similar to the relations of the Snyder and Yang spaces. Furthermore, using a reparametrized relativistic particle we obtain a realization of the Snyder type spaces and we construct an action for them.},
doi = {10.1103/PHYSREVD.75.065008},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • We explicitly derive, following a Noether-like approach, the criteria for preserving Poincare invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that, interpreted appropriately, Poincare invariance holds. The analysis is performed in both the commutative as well as noncommutative descriptions and a compatibility between the two is also established.
  • We study issues of Lorentz violation symmetry in the context of the recently proposed theory of noncommutative fields [J. Carmona, J. L. Cortes, J. Gamboa, and F. Mendes, J. High Energy Phys. 03 (2003) 058; Phys. Lett. B 565, 222 (2003).], using the soldering formalism. To this end a noncommutative chiral boson with a deformed algebra [A. Das, J. Gamboa, F. Mendes, and J. Lopes-Sarrion, J. High Energy Phys. 05 (2004) 022.], used to study these notions in D=2, is properly generalized. We verify, also for this larger group of theories that, although the structure of the Lorentz group ismore » preserved, the velocity of light is scaled by a function of the deformation parameter, as recently claimed. However, we found a subset of models where the velocity of propagation is maintained in spite of the presence of the deformed algebra. Effects of a preferred frame of reference manifest by the presence of birefringence were also studied in the chiral boson framework leading to the scalar sector of the extended standard model recently proposed.« less
  • In this paper we deal with the issue of Lorentz symmetry breaking in quantum field theories formulated in a noncommutative space-time. We show that, unlike in some recent analysis of quantum gravity effects, supersymmetry does not protect the theory from the large Lorentz-violating effects arising from the loop corrections. We take advantage of the noncommutative Wess-Zumino model to illustrate this point.
  • We show that Lorentz symmetry is generally absent for noncommutative (Abelian) gauge theories and obtain a compact formula for the divergence of the Noether currents that allows a thorough study of this instance of symmetry violation. We use that formula to explain why the results of ''Noncommutative gauge theories and Lorentz symmetry'', Phys. Rev. D 70, 125004 (2004) by R. Banerjee, B. Chakraborty, and K. Kumar, interpreted there as new criteria for Lorentz invariance, are in fact just a particular case of the general expression for Lorentz violation obtained here. Finally, it is suggested that the divergence formula should holdmore » in a vast class of cases, such as, for instance, the standard model extension.« less
  • This is a reply to the preceding 'Comment on 'Noncommutative gauge theories and Lorentz symmetry'', Phys. Rev. D 77, 048701 (2008) by Alfredo Iorio.