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arXiv · 1004.0621

Scalar field theory in Snyder space-time: alternatives

Florian Girelli·Etera R. Livine
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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 $\SO(3,1)/\SO(3)$, but our results extend to any dimension and signature.

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Florian Girelli, Etera R. Livine. 2010-04-05. Scalar field theory in Snyder space-time: alternatives. https://doi.org/10.1007/jhep03(2011)132

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