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arXiv · 2401.06660

Fractional index of Bargmann-Fock space and Landau levels

Guo Chuan Thiang
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Abstract

The lowest Landau level Hilbert space, or the Bargmann-Fock space, admits a quantized trace for the commutator of its position coordinate operators. We exploit the Carey-Pincus theory of principal functions of trace class commutators to probe this integer quantization result further, and uncover a hidden rational structure in the higher-order commutator-traces. This shows how exact fractional quantization can occur whenever exact integral quantization does.

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Guo Chuan Thiang. 2024-01-12. Fractional index of Bargmann-Fock space and Landau levels. https://doi.org/10.1016/j.geomphys.2024.105415

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