Deformations of the Canonical Commutation Relations and Metric Structures

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2014
• Main Authors: D'Andrea, F., Lizzi, F., Martinetti, P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146655
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Deformations of the Canonical Commutation Relations and Metric Structures / F. D'Andrea, F. Lizzi, P. Martinetti // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 33 назв. — англ.

Using Connes distance formula in noncommutative geometry, it is possible to retrieve the Euclidean distance from the canonical commutation relations of quantum mechanics. In this note, we study modifications of the distance induced by a deformation of the position-momentum commutation relations. We...