Scalar field theory in Snyder space-time: alternatives
Abstract
We construct two types of scalar field theory on Snyder space-time. The first one is based on the natural momenta addition inherent to the coset momentum space. This construction uncovers a non-associative deformation of the Poincar\'e symmetries. The second one considers Snyder space-time as a subspace of a larger non-commutative space. We discuss different possibilities to restrict the extra-dimensional scalar field theory to a theory living only on Sndyer space-time and present the consequences of these restrictions on the Poincar\'e symmetries. We show moreover how the non-associative approach and the Doplicher-Fredenhagen-Roberts space can be seen as specific approximations of the extra-dimensional theory. These results are obtained for the 3d Euclidian Snyder space-time constructed from , but our results extend to any dimension and signature.
Keywords
Cite
@article{arxiv.1004.0621,
title = {Scalar field theory in Snyder space-time: alternatives},
author = {Florian Girelli and Etera R. Livine},
journal= {arXiv preprint arXiv:1004.0621},
year = {2011}
}
Comments
24 pages.