Quantum 2025 – scientific programme
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TUE: Tuesday Contributed Sessions
TUE 10: Foundational / Mathematical Aspects – Rigorous Results
TUE 10.2: Talk
Tuesday, September 9, 2025, 14:30–14:45, ZHG103
In a closed universe, orbital angular momentum has non-integer values — •Daniel Burgarth1 and Paolo Facchi2 — 1Friedrich Alexander University — 2Bari University
We show that the spectrum of orbital angular momentum in quantum mechanics is the union of two parts when the underlying space has periodic boundaries. While the first part corresponds to the usual textbook integer quantized values, the second is a continuous band arising from the edge of space with respect to the center of rotation. The spectrum thus contains not only half-integer values (often thought impossible for orbital angular momentum), but even irrational ones. This effect is independent of the size of space. We argue that such spectral components would be invisible in the laboratory but might nonetheless have observable consequences on the cosmic scale.
Keywords: Angular Momentum; Spectral Theory; Mathematical Physics; Foundations; Quantum Theory