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The Action Functional for Moyal Planes

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Abstract

Modulo some natural generalizations to noncompact spaces, we show in this Letter that Moyal planes are nonunital spectral triples in the sense of Connes. The action functional of these triples is computed, and we obtain the expected result, i.e. the noncommutative Yang–Mills action associated with the Moyal product. In particular, we show that Moyal gauge theory naturally fits into the rigorous framework of noncommutative geometry.

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Authors and Affiliations

  1. Unité Propre de Recherche 7061, CNRS–Luminy, Case 907, Centre de Physique Théorique, 13288, Marseille Cedex 9, France

    Victor Gayral

  2. Université de Provence, France

    Victor Gayral

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  1. Victor Gayral
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Gayral, V. The Action Functional for Moyal Planes. Letters in Mathematical Physics 65, 147–157 (2003). https://doi.org/10.1023/B:MATH.0000004380.57824.94

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  • DOI: https://doi.org/10.1023/B:MATH.0000004380.57824.94

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