On Dirac equations on phase spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912830206246912 |
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| author | Popov, Alexander D. |
| author_facet | Popov, Alexander D. |
| contents | We consider Dirac equations on relativistic phase spaces $T^*{\mathbb R}^{p-1,1}$, where ${\mathbb R}^{p-1,1}$ is Minkowski space with $p=2,4$. We use the geometric quantization approach in which the wave functions are polarized sections of a complex line bundle $L_{\sf{v}}$ over $T^*{\mathbb R}^{p-1,1}$. The covariant derivatives with connection $A_{\sf{vac}}$ in this bundle define canonical commutation relations. Fermions are charged with respect to the field $A_{\sf{vac}}$, so lifting the Dirac equations from space-time ${\mathbb R}^{p-1,1}$ to phase space $T^*{\mathbb R}^{p-1,1}$ results in their solutions being localized in the space ${\mathbb R}^{p-1}$ or in space-time ${\mathbb R}^{p-1,1}$. We describe the explicit form of these solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06404 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Dirac equations on phase spaces Popov, Alexander D. High Energy Physics - Theory Mathematical Physics Quantum Physics We consider Dirac equations on relativistic phase spaces $T^*{\mathbb R}^{p-1,1}$, where ${\mathbb R}^{p-1,1}$ is Minkowski space with $p=2,4$. We use the geometric quantization approach in which the wave functions are polarized sections of a complex line bundle $L_{\sf{v}}$ over $T^*{\mathbb R}^{p-1,1}$. The covariant derivatives with connection $A_{\sf{vac}}$ in this bundle define canonical commutation relations. Fermions are charged with respect to the field $A_{\sf{vac}}$, so lifting the Dirac equations from space-time ${\mathbb R}^{p-1,1}$ to phase space $T^*{\mathbb R}^{p-1,1}$ results in their solutions being localized in the space ${\mathbb R}^{p-1}$ or in space-time ${\mathbb R}^{p-1,1}$. We describe the explicit form of these solutions. |
| title | On Dirac equations on phase spaces |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2402.06404 |