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Advances in High Energy Physics
Volume 2017, Article ID 4731050, 11 pages
https://doi.org/10.1155/2017/4731050
Research Article

Space-Time Defects and Group Momentum Space

1Dipartimento di Fisica and INFN, “Sapienza” University of Rome, P.le A. Moro 2, 00185 Roma, Italy
2Institute of Theoretical Physics, University of Wrocław, Pl. M. Borna 9, 50-204 Wrocław, Poland

Correspondence should be addressed to Tomasz Trześniewski; lp.corw.inu.tfi@tbwbt

Received 11 May 2017; Accepted 16 July 2017; Published 17 August 2017

Academic Editor: Angel Ballesteros

Copyright © 2017 Michele Arzano and Tomasz Trześniewski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

We study massive and massless conical defects in Minkowski and de Sitter spaces in various space-time dimensions. The energy momentum of a defect, considered as an (extended) relativistic object, is completely characterized by the holonomy of the connection associated with its space-time metric. The possible holonomies are given by Lorentz group elements, which are rotations and null rotations for massive and massless defects, respectively. In particular, if we fix the direction of propagation of a massless defect in -dimensional Minkowski space, then its space of holonomies is a maximal Abelian subgroup of the AN group, which corresponds to the well known momentum space associated with the -dimensional -Minkowski noncommutative space-time and -deformed Poincaré algebra. We also conjecture that massless defects in -dimensional de Sitter space can be analogously characterized by holonomies belonging to the same subgroup. This shows how group-valued momenta related to four-dimensional deformations of relativistic symmetries can arise in the description of motion of space-time defects.