Approximate Synthetic Spectra of Quantum Systems Associated with Compact Lie Groups

Abstract:How can noncommuting quantum observables retain the geometry of a classical phase space? Motivated by Mumford's question on approximately macroscopically unique (AMU) states and the work of Lin and Wang, we study synthetic spectra of position--momentum and angular-momentum systems. Under the hypotheses of their AMU theorems, nonempty synthetic spectra yield AMU states. For sufficiently small $\hbar$, the position--momentum spectrum fills the plane, while the angular-momentum spectrum contains any prescribed ball. The latter calculation leads to compact Lie groups: we prove that highest-weight coadjoint orbits lie in regional synthetic spectra under an explicit variance bound. Function-space representations of $SU(n)$, $SO(n)$, and $Sp(n)$ provide further examples.

Quantum Physics (quant-ph); Operator Algebras (math.OA)

arXiv:2611.04306 [quant-ph]

(or arXiv:2611.04306v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.04306 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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