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Given the importance of quantum reference frames (QRFs) to both quantum andgravitational physics, it is pertinent to develop a systematic method forswitching between the descriptions of physics relative to different choices ofQRFs, which is valid in both fields. Here we continue with such a unifyingapproach, begun in arxiv:1809.00556, whose key ingredient is a symmetryprinciple, which enforces physics to be relational. Thanks to gauge relatedredundancies, this leads to a perspective-neutral structure which contains allframe choices at once and via which frame perspectives can be consistentlyswitched. Formulated in the language of constrained systems, theperspective-neutral structure is the constraint surface classically and thegauge invariant Hilbert space in the Dirac quantized theory. By contrast, aperspective relative to a specific frame corresponds to a gauge choice and theassociated reduced phase and Hilbert space. QRF changes thus amount to a gaugetransformation. We show that they take the form of `quantum coordinatechanges'. We illustrate this in a general mechanical model, namely therelational $N$-body problem in 3D space with rotational and translationalsymmetry. This model is especially interesting because it features the Gribovproblem so that globally valid gauge fixing conditions, and hence relationalframe perspectives, are absent. The constraint surface is topologicallynon-trivial and foliated by 3-, 5- and 6-dimensional gauge orbits, where thelower dimensional orbits are a set of measure zero. The $N$-body problem alsodoes not admit globally valid canonically conjugate pairs of Dirac observables.These challenges notwithstanding, we exhibit how one can construct the QRFtransformations for the 3-body problem. Our construction also sheds new lighton the generic inequivalence of Dirac and reduced quantization through itsinterplay with QRF perspectives.

Switching quantum reference frames in the N-body problem and the absence of global relational perspectives