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Communications in Mathematical Physics

, Volume 246, Issue 3, pp 569–623 | Cite as

Moyal Planes are Spectral Triples

  • V. Gayral
  • J.M. Gracia-Bondía
  • B. Iochum
  • T. Schücker
  • J.C. Várilly
Article

Abstract

Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory, the spaces R2N endowed with Moyal products are intensively investigated. Some physical applications, such as the construction of noncommutative Wick monomials and the computation of the Connes–Lott functional action, are given for these noncommutative hyperplanes.

Keywords

Field Theory Quantum Field Theory Physical Application Functional Action Spectral Triple 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • V. Gayral
    • 1
    • 2
  • J.M. Gracia-Bondía
    • 3
  • B. Iochum
    • 1
    • 2
  • T. Schücker
    • 1
    • 2
  • J.C. Várilly
    • 4
    • 5
  1. 1.Centre de Physique ThéoriqueCNRS–LuminyMarseille Cedex 9France
  2. 2.Université de ProvenceFrance
  3. 3.Departamento de FísicaUniversidad de Costa RicaSan PedroCosta Rica
  4. 4.Departamento de MatemáticasUniversidad de Costa RicaSan PedroCosta Rica
  5. 5.Regular Associate of the Abdus Salam ICTPTriesteItaly

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