Noncommutative Geometry and Field Theory

  • Dmitri Fursaev
  • Dmitri Vassilevich
Part of the Theoretical and Mathematical Physics book series (TMP)


After a short motivation for noncommutativity, a noncommutative (NC) Moyal product is introduced and its’ basic properties are established. Then, the heat kernel expansion for Laplace type operators on the Moyal spaces is constructed. This expansion, together with the results of Chap.  6, is then used to analyse one-loop divergences in NC ϕ 4 theory on the kink background. A short introduction into NC geometry of Connes is presented, and the spectral action for electromagnetic field on the Moyal plane is calculated.


Dirac Operator Heat Kernel Star Product Noncommutative Geometry Spectral Action 
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 Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Dubna International UniversityDubnaRussia
  2. 2.CMCCUniversidade Federal do ABCSanto AndreBrazil

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