We explore the possibility to extend the Heisenberg’s uncertainty principle to a nonlinear extension of the quantum algebra related to a functional operator of the momenta as [Formula: see text]. We show that such an extension of quantum mechanics is intimately connected to the non-commutative space-time algebra and the Lorentz symmetry deformations. We show that a large class of [Formula: see text] models can introduce superluminal modes in the quantized theories. We also show that the Hořava–Lifshitz theory is related to a large class of [Formula: see text] Quantum Mechanics.

中文翻译：

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ℱ(P) 量子力学

我们探索将海森堡的不确定性原理扩展到与动量的函数算子相关的量子代数的非线性扩展的可能性，如[公式：见正文]。我们表明，量子力学的这种扩展与非交换时空代数和洛伦兹对称变形密切相关。我们展示了一大类 [公式：见正文] 模型可以在量子化理论中引入超光速模式。我们还表明，Hořava-Lifshitz 理论与一大类 [公式：见正文] 量子力学有关。