Monopole harmonics on $\mathbb{CP}^{n-1}$
We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the $\mathbb{CP}^{n-1}$ manifold in the presence of a background monopole-like gauge field. The states form degenerate $SU(n)$ multiplets and their wa...
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| Format: | Article |
| Language: | English |
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SciPost
2023-11-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.5.195 |
| _version_ | 1797628026992721920 |
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| author | Dmitri Bykov, Andrei Smilga |
| author_facet | Dmitri Bykov, Andrei Smilga |
| author_sort | Dmitri Bykov, Andrei Smilga |
| collection | DOAJ |
| description | We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the $\mathbb{CP}^{n-1}$ manifold in the presence of a background monopole-like gauge field. The states form degenerate $SU(n)$ multiplets and their wave functions acquire a very simple form being expressed via homogeneous coordinates. Their relationship to multidimensional orthogonal polynomials of a special kind is discussed. By the well-known isomorphism between the twisted Dolbeault and Dirac complexes, our construction also gives the eigenfunctions and eigenvalues of the Dirac operator on complex projective spaces in a monopole background. |
| first_indexed | 2024-03-11T10:33:39Z |
| format | Article |
| id | doaj.art-80bec8b78c8644df82b8f0497fad03c8 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-11T10:33:39Z |
| publishDate | 2023-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-80bec8b78c8644df82b8f0497fad03c82023-11-14T13:08:18ZengSciPostSciPost Physics2542-46532023-11-0115519510.21468/SciPostPhys.15.5.195Monopole harmonics on $\mathbb{CP}^{n-1}$Dmitri Bykov, Andrei SmilgaWe find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the $\mathbb{CP}^{n-1}$ manifold in the presence of a background monopole-like gauge field. The states form degenerate $SU(n)$ multiplets and their wave functions acquire a very simple form being expressed via homogeneous coordinates. Their relationship to multidimensional orthogonal polynomials of a special kind is discussed. By the well-known isomorphism between the twisted Dolbeault and Dirac complexes, our construction also gives the eigenfunctions and eigenvalues of the Dirac operator on complex projective spaces in a monopole background.https://scipost.org/SciPostPhys.15.5.195 |
| spellingShingle | Dmitri Bykov, Andrei Smilga Monopole harmonics on $\mathbb{CP}^{n-1}$ SciPost Physics |
| title | Monopole harmonics on $\mathbb{CP}^{n-1}$ |
| title_full | Monopole harmonics on $\mathbb{CP}^{n-1}$ |
| title_fullStr | Monopole harmonics on $\mathbb{CP}^{n-1}$ |
| title_full_unstemmed | Monopole harmonics on $\mathbb{CP}^{n-1}$ |
| title_short | Monopole harmonics on $\mathbb{CP}^{n-1}$ |
| title_sort | monopole harmonics on mathbb cp n 1 |
| url | https://scipost.org/SciPostPhys.15.5.195 |
| work_keys_str_mv | AT dmitribykovandreismilga monopoleharmonicsonmathbbcpn1 |