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Abstract: We study the noncommutative geometry of the Moyal plane from a metric pointof view. Starting from a non compact spectral triple based on the Moyaldeformation A of the algebra of Schwartz functions on R^2, we explicitlycompute Connes- spectral distance between the pure states of A corresponding toeigenfunctions of the quantum harmonic oscillator. For other pure states, weprovide a lower bound to the spectral distance, and show that the latest is notalways finite. As a consequence, we show that the spectral triple 20 is not aspectral metric space in the sense of 5. This motivates the study oftruncations of the spectral triple, based on M nC with arbitrary integer n,which turn out to be compact quantum metric spaces in the sense of Rieffel.Finally the distance is explicitly computed for n=2.



Autor: Eric Cagnache, Francesco D'Andrea, Pierre Martinetti, Jean-Christophe Wallet

Fuente: https://arxiv.org/







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