The action functional for Moyal planes

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, ie the noncommutative Yang-Mills action associated with the Moyal product. In particular, we show that Moyal gauge theory naturally fit into the rigorous framework of noncommutative geometry.

latex, 10 pages

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• Infinitely many star products to play with
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Cited by in corpus (5)

• The spectral action for Moyal planes
• Minimal length in quantum space and integrations of the line element in Noncommutative Geometry
• Spectral action and big desert
• Noncommutative Induced Gauge Theories on Moyal Spaces
• Spectral Distances: Results for Moyal Plane and Noncommutative Torus