Geometry of the Grosse-Wulkenhaar model

Article

Abstract

We analyze properties of a family of finite-matrix spaces obtained by a truncation of the Heisenberg algebra and we show that it has a three-dimensional, noncommutative and curved geometry. Further, we demonstrate that the Heisenberg algebra can be described as a two-dimensional hyperplane embedded in this space. As a consequence of the given construction we show that the Grosse-Wulkenhaar (renormalizable) action can be interpreted as the action for the scalar field on a curved background space. We discuss the generalization to four dimensions.

Keywords

Non-Commutative Geometry Nonperturbative Effects Differential and Algebraic Geometry 

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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Faculty of PhysicsUniversity of BelgradeBelgradeSerbia
  2. 2.Institute for Theoretical PhysicsVienna University of TechnologyViennaAustria

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