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

S. Naka, H. Toyoda, T. Takanashi, Eizo Umezawa

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
Article number043B03
JournalProgress of Theoretical and Experimental Physics
Volume2014
Issue number4
DOIs
Publication statusPublished - 01-01-2014

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symmetry
wave equations
relativity
generators

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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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-Poincar{\'E} 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.",
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Noncommutative spacetime realized in AdSn+1 space : Nonlocal field theory out of noncommutative spacetime. / Naka, S.; Toyoda, H.; Takanashi, T.; Umezawa, Eizo.

In: Progress of Theoretical and Experimental Physics, Vol. 2014, No. 4, 043B03, 01.01.2014.

Research output: Contribution to journalArticle

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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.

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