2010/03/31 by Marco Valerio Battisti, Stjepan Meljanac · 1 citation
Physics and Astronomy · #hep-th #gr-qc
paper · pdf · doi:10.1103/physrevd.82.024028
published as Phys.Rev.D82:024028,2010 · 10 pages; v2: introduction rewritten, co-algebraic analysis improved, references added; to appear in PRD
arxiv created 2010/06/23 · arxiv updated 2014/11/20
We construct a scalar field theory on the Snyder non-commutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincaré algebra is undeformed. The Lorentz sector is undeformed at both algebraic and co-algebraic level, but the co-product for momenta (defining the star-product) is non-co-associative. The Snyder-deformed Poincaré group is described by a non-co-associative Hopf algebra. The definition of the interacting theory in terms of a non-associative star-product is thus questionable. We avoid the non-associativity by the use of a space-time picture based on the concept of realization of a non-commutative geometry. The two main results we obtain are: (i) the generic (namely for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a non-ambiguous self interacting scalar field theory on this space-time. The first order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.