Noncommutative Spacetime Realized in $Ad{S}_{n+1}$ Space

Abstract

In $\kappa$-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 ${\kappa }^{-1}$, which is a universal constant other than the light velocity under the $\kappa$-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) generators in 4-dimensional de Sitter space. In this paper, we try to construct a nonommutative spacetime having commutative n-dimensional Minkowski spacetime based on $Ad{S}_{n+1}$ 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.

16 pages, 4 figures

References in corpus (5)

• Introduction to Doubly Special Relativity
• From noncommutative kappa-Minkowski to Minkowski space-time
• Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity
• Low-energy constraints on kappa-Minkowski extension of the Standard Model
• Q-Deformed Bi-Local Fields

Cited by in corpus (1)

• An Approach to Yukawa's Elementary Domain Based on $\mbox{AdS}_5$ Spacetime