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arXiv · 2503.23146

Reduced Yang model and noncommutative geometry of curved spacetime

S. Meljanac·S. Mignemi
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Abstract

The Yang model describes a noncommutative geometry in a curved spacetime by means of an orthogonal algebra $o(1,5)$, whose 15 generators are identified with phase space variables and Lorentz generators together with an additional scalar generator. In this paper we show that it is possible to define a nonlinear algebra with the same structure, but with only 14 generators, that better fits in phase space. The fifteenth generator of the Yang algebra can then be written as a function of the squares of the others. As a simple application, we also consider the problem of the quantum harmonic oscillator in this theory, calculating the energy spectrum in the one- and three-dimensional nonrelativistic versions of the model.

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S. Meljanac, S. Mignemi. 2025-03-29. Reduced Yang model and noncommutative geometry of curved spacetime. https://arxiv.org/abs/2503.23146

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