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TUE: Tuesday Contributed Sessions

TUE 10: Foundational / Mathematical Aspects – Rigorous Results

TUE 10.2: Vortrag

Dienstag, 9. September 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