Double Quantization

Giulia Gubitosi; Fedele Lizzi; José Javier Relancio; Patrizia Vitale

doi:10.1103/physrevd.105.126013

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arXiv · 2112.11401

Double Quantization

Giulia Gubitosi·Fedele Lizzi·José Javier Relancio·Patrizia Vitale

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Abstract

In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties. A possible way to take into account these quantum effects is through a noncommutativity of spacetime coordinates. In the literature, there is not a clear way to describe at the same time a noncommutativity of spacetime and the phase-space noncommutativity of quantum mechanics. In this paper we address this issue by constructing a Drinfel'd twist in phase space which deals with both quantizations. This method can be applied to a noncommutativity which involves only space, leaving time aside. We apply our construction to the so-called $\lambda$-Minkwoski and $\mathbb{R}^3_\lambda$ noncommutative spaces.

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Giulia Gubitosi, Fedele Lizzi, José Javier Relancio, Patrizia Vitale. 2021-12-21. Double Quantization. https://doi.org/10.1103/physrevd.105.126013

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