Description
Title: Quantum coordinate transformations via matter fields for quantum spacetime
Abstract: A central challenge in quantum gravity is to formulate a theory without presupposing a background spacetime. Such a description requires relational observables and a genuinely quantum generalisation of diffeomorphisms. Here we associate coordinate systems with sets of four dynamical scalar fields, whose stress-energy tensors contribute to the constraints of linearised quantum gravity.
Such quantum coordinate fields (QCFs) extend the notion of quantum reference frames and enable a relational description of other physical systems. By generalizing the perspective-neutral construction of quantum reference frames, we show that relational, gauge invariant observables admit a description in each QCF perspective, and derive consistent transformations between perspectives. The resulting unitary maps implement passive or active, local quantum coordinate changes, yielding quantum linearized diffeomorphisms beyond superpositions of classical ones. We further discuss the operational aspects of relational observables, the conceptual distinction between QCFs and quantum reference frames, and identify the difference between QCFs transformations and the superposition of classical diffeomorphisms.