Quantum conformal symmetries for spacetimes in superposition

Understand

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.