Massless Dirac equation on spinor bundles over real hyperbolic spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929608859844608 |
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| author | Meng, Long Zhang, Hong-Wei Zhang, Junyong |
| author_facet | Meng, Long Zhang, Hong-Wei Zhang, Junyong |
| contents | We prove a sharp-in-time dispersive estimate of the Dirac equation on spinor bundles over the real hyperbolic space. Compared with the Euclidean counterparts, our result shows that the dispersive estimate differs between short and long times, reflecting the intuitive influence of negative curvature on the dispersion. Moreover, the well-known equivalence between dispersive estimates for Dirac and wave propagators in the Euclidean setting no longer holds in this context. This finding suggests that spinor fields are affected by the geometry at infinity of the manifold. As a key application, we establish an improved global-in-time Strichartz estimate, in the sense that there is no loss of angular derivatives and the admissible set is larger than previously known results in other settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Massless Dirac equation on spinor bundles over real hyperbolic spaces Meng, Long Zhang, Hong-Wei Zhang, Junyong Analysis of PDEs 35Q41, 35L05, 35R01 We prove a sharp-in-time dispersive estimate of the Dirac equation on spinor bundles over the real hyperbolic space. Compared with the Euclidean counterparts, our result shows that the dispersive estimate differs between short and long times, reflecting the intuitive influence of negative curvature on the dispersion. Moreover, the well-known equivalence between dispersive estimates for Dirac and wave propagators in the Euclidean setting no longer holds in this context. This finding suggests that spinor fields are affected by the geometry at infinity of the manifold. As a key application, we establish an improved global-in-time Strichartz estimate, in the sense that there is no loss of angular derivatives and the admissible set is larger than previously known results in other settings. |
| title | Massless Dirac equation on spinor bundles over real hyperbolic spaces |
| topic | Analysis of PDEs 35Q41, 35L05, 35R01 |
| url | https://arxiv.org/abs/2411.19597 |