Noncommutative spacetime realized in Ad Sn+1 space: Nonlocal field theory out of noncommutative spacetime

S. Naka, H. Toyoda, T. Takanashi, E. Umezawa
2014 Progress of Theoretical and Experimental Physics  
In κ-Minkowski spacetime, the coordinates are Lie algebraic elements such that time and space coordinates do not commute, whereas space coordinates commute each other. The non-commutativity is proportional to a Planck-length-scale constant κ^-1, which is a universal constant other than the light velocity under the κ-Poincare transformation. In this sense, the spacetime has a structure called as "Doubly Special Relativity". Such a noncommutative structure is known to be realized by SO(1,4)
more » ... tors in 4-dimensional de Sitter space. In this paper, we try to construct a nonommutative spacetime having commutative n-dimensional Minkowski spacetime based on AdS_n+1 space with SO(2,n) symmetry. We also study an invariant wave equation corresponding to the first Casimir invariant of this symmetry as a non-local field equation expected to yield finite loop amplitudes.
doi:10.1093/ptep/ptu022 fatcat:vuncpifprvgmfc62pfo4lvthl4