Holomorphic Quantization in Constant Curvature Backgrounds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917296736305152 |
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| author | Bykov, Dmitri Krivorol, Viacheslav |
| author_facet | Bykov, Dmitri Krivorol, Viacheslav |
| contents | We present a holomorphic quantization scheme for free point particles on two-dimensional constant curvature Riemannian backgrounds. The procedure is based on a Lagrangian embedding of the particle configuration space into a product of coadjoint orbits of the background isometry group. Examples are provided by particles on the plane, torus, sphere, and hyperbolic plane, with or without a monopole field. We elaborate the method by recovering the Hamiltonian spectrum and the wave functions on such spaces. As a by-product, we obtain a geometric and physical interpretation of Repka's result on the decomposition of tensor products of $\mathbf{SL}(2,\mathbb{R})$ discrete series representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22984 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holomorphic Quantization in Constant Curvature Backgrounds Bykov, Dmitri Krivorol, Viacheslav High Energy Physics - Theory Mathematical Physics We present a holomorphic quantization scheme for free point particles on two-dimensional constant curvature Riemannian backgrounds. The procedure is based on a Lagrangian embedding of the particle configuration space into a product of coadjoint orbits of the background isometry group. Examples are provided by particles on the plane, torus, sphere, and hyperbolic plane, with or without a monopole field. We elaborate the method by recovering the Hamiltonian spectrum and the wave functions on such spaces. As a by-product, we obtain a geometric and physical interpretation of Repka's result on the decomposition of tensor products of $\mathbf{SL}(2,\mathbb{R})$ discrete series representations. |
| title | Holomorphic Quantization in Constant Curvature Backgrounds |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2602.22984 |