Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension of the quantum reference frame formalism to address this question for the Klein-Gordon field residing on a superposition of conformally equivalent metrics. Based on the group structure of “quantum conformal transformations'', we construct an explicit quantum operator that can map states describing a quantum field on a superposition of spacetimes to states representing a quantum field with a superposition of masses on a Minkowski background. This constitutes an extended symmetry principle, namely invariance under quantum conformal transformations. The latter allows to build an understanding of superpositions of diffeomorphically non-equivalent spacetimes by relating them to a more intuitive superposition of quantum fields on curved spacetime. Furthermore, it can be used to import the phenomenon of particle production in curved spacetime to its conformally equivalent counterpart, thus revealing new features in modified Minkowski spacetime.

中文翻译：

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叠加时空的量子共形对称性


如果没有完整的量子引力理论，量子场和量子粒子在时空叠加中的行为问题似乎超出了理论和实验研究的范围。在这里，我们使用量子参考系形式主义的扩展来回答位于共形等效度量叠加上的 Klein-Gordon 场的这个问题。基于“量子共形变换”的群结构，我们构建了一个显式量子算子，它可以将描述时空叠加上的量子场的状态映射到表示在 Minkowski 背景上具有质量叠加的量子场的状态。这构成了一个扩展对称原理，即量子共形变换下的不变性。后者允许通过将差分非等效时空的叠加与弯曲时空中更直观的量子场叠加联系起来，从而建立对微分同态非等效时空叠加的理解。此外，它可以用于将弯曲时空中粒子产生的现象导入到其共形等效的对应物中，从而揭示修正的 Minkowski 时空的新特征。