Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF transformations for Lorentz symmetry is still lacking. The present work aims to fill this gap. We first introduce a reformulation of relativistic quantum mechanics independent of any notion of preferred temporal slicing. Based on this, we define transformations that switch between the perspectives of different relativistic QRFs. We introduce a notion of ''quantum Lorentz transformations'' and ''superposition of Lorentz boosts'', acting on the external degrees of freedom of a quantum particle. We analyse two effects, superposition of time dilations and superposition of length contractions, that arise only if the reference frames exhibit both relativistic and quantum-mechanical features. Finally, we discuss how the effects could be observed by measuring the wave-packet extensions from relativistic QRFs.

中文翻译：

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洛伦兹对称性的量子参考系


自从首次引入以来，量子参考系 (QRF) 变换已被广泛讨论，将物理定律的协方差推广到量子域。尽管取得了重要进展，但仍然缺乏洛伦兹对称性的 QRF 变换公式。目前的工作旨在填补这一空白。我们首先引入独立于任何首选时间切片概念的相对论量子力学的重新表述。基于此，我们定义了在不同相对论 QRF 的视角之间切换的变换。我们引入了“量子洛伦兹变换”和“洛伦兹增强叠加”的概念，作用于量子粒子的外部自由度。我们分析了两种效应，即时间膨胀的叠加和长度收缩的叠加，这两种效应只有在参考系同时表现出相对论和量子力学特征时才会出现。最后，我们讨论如何通过测量相对论 QRF 的波包扩展来观察效应。