### Abstract

In κ-Minkowski spacetime, the coordinates are Lie algebraic elements such that time and space coordinates do not commute, whereas space coordinates commute with each other. The noncommutativity is proportional to a Planck-length-scale constant κ^{-1}, which is a universal constant other than the velocity of light, under the ?κ-PoincarÉ transformation. In this sense, the spacetime has a structure called "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 noncommutative spacetime having a 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 nonlocal field equation expected to yield finite loop amplitudes.

Original language | English |
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Article number | 043B03 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2014 |

Issue number | 4 |

DOIs | |

Publication status | Published - 04-2014 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

_{n+1}space: Nonlocal field theory out of noncommutative spacetime.

*Progress of Theoretical and Experimental Physics*,

*2014*(4), [043B03]. https://doi.org/10.1093/ptep/ptu022