Double Quantization
- URL: http://arxiv.org/abs/2112.11401v3
- Date: Mon, 24 Jul 2023 10:20:49 GMT
- Title: Double Quantization
- Authors: Giulia Gubitosi, Fedele Lizzi, Jos\'e Javier Relancio, Patrizia Vitale
- Abstract summary: In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties.
There is not a clear way to describe at the same time a noncommutativity of spacetime and the phase-space noncommutativity of quantum mechanics.
We apply our construction to the so-called $lambda$-Minkwoski and $mathbbR3_lambda$ noncommutative spaces.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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