Field theories with homogenous momentum space
arXiv:0910.3107 · doi:10.1063/1.3284372
Abstract
We discuss the construction of a scalar field theory with momentum space given by a coset. By introducing a generalized Fourier transform, we show how the dual scalar field theory actually lives in Snyder's space-time. As a side-product we identify a star product realization of Snyder's non-commutative space, but also the deformation of the Poincare symmetries necessary to have these symmetries realized in Snyder's space-time. A key feature of the construction is that the star product is non-associative.
9 pages, To appear in the Proceedings of the XXV Max Born Symposium, "The Planck Scale", Wroclaw, Poland, July 2009