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 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.
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ArXiv ePrint: 1004.0621
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Girelli, F., Livine, E.R. Scalar field theory in Snyder space-time: alternatives. J. High Energ. Phys. 2011, 132 (2011). https://doi.org/10.1007/JHEP03(2011)132
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DOI: https://doi.org/10.1007/JHEP03(2011)132