2010/04/05 by Florian Girelli, Etera R. Livine · 1 citation
Physics and Astronomy · #hep-th #gr-qc
paper · pdf · doi:10.1007/jhep03(2011)132
published as JHEP 1103:132,2011 · 24 pages.
arxiv created 2010/04/05 · arxiv updated 2011/03/31
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 Poincaré 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 Poincaré 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 \SO(3,1)/\SO(3), but our results extend to any dimension and signature.