Fractional index of Bargmann-Fock space and Landau levels
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912178858098688 |
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| author | Thiang, Guo Chuan |
| author_facet | Thiang, Guo Chuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional index of Bargmann-Fock space and Landau levels Thiang, Guo Chuan Mathematical Physics Mesoscale and Nanoscale Physics 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. |
| title | Fractional index of Bargmann-Fock space and Landau levels |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2401.06660 |