### 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 |
---|---|

Article number | 043B03 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2014 |

Issue number | 4 |

DOIs | |

Publication status | Published - 01-01-2014 |

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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

}

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

*Progress of Theoretical and Experimental Physics*, vol. 2014, no. 4, 043B03. https://doi.org/10.1093/ptep/ptu022

**Noncommutative spacetime realized in AdS _{n+1} space : Nonlocal field theory out of noncommutative spacetime.** / Naka, S.; Toyoda, H.; Takanashi, T.; Umezawa, Eizo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Noncommutative spacetime realized in AdSn+1 space

T2 - Nonlocal field theory out of noncommutative spacetime

AU - Naka, S.

AU - Toyoda, H.

AU - Takanashi, T.

AU - Umezawa, Eizo

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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 AdSn+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.

AB - 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 AdSn+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.

UR - http://www.scopus.com/inward/record.url?scp=84898487913&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898487913&partnerID=8YFLogxK

U2 - 10.1093/ptep/ptu022

DO - 10.1093/ptep/ptu022

M3 - Article

AN - SCOPUS:84898487913

VL - 2014

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 4

M1 - 043B03

ER -

_{n+1}space: Nonlocal field theory out of noncommutative spacetime. Progress of Theoretical and Experimental Physics. 2014 Jan 1;2014(4). 043B03. https://doi.org/10.1093/ptep/ptu022