On the tensorial structure of general covariant quantum systems
arxiv(2023)
Abstract
The definition of a quantum system requires a Hilbert space, a way to define
the dynamics, and an algebra of observables. The structure of the observable
algebra is related to a tensor product decomposition of the Hilbert space and
represents the composition of the system by subsystems. It has been remarked
that the Hamiltonian may determine this tensor product structure. Here we
observe that this fact may lead to questionable consequences in some cases, and
does extend to the more general background-independent case, where the
Hamiltonian is replaced by a Hamiltonian constraint. These observations
reinforces the idea that specifying the observables and the way they interplay
with the dynamics, is essential to define a quantum theory. We also reflect on
the general role that system decomposition has in the quantum theory.
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