Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.13335 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916906232971264 |
|---|---|
| author | Tiwari, S C |
| author_facet | Tiwari, S C |
| contents | Hodge theorem and harmonic spinors are studied in a physics-oriented approach in the present paper. New mathematical results on the harmonic spinors are as follows. Harmonic spinors defined by partial differential operators could be of two types: trivial without topological defects, and having nontrivial topological structures, for example, phase singularities or phase vortices. There could exist a nontrivial harmonic vector field associated with nontrivial harmonic spinor, for example, ${\bf v}_{vortex}$ associated with Weyl 2-spinor. The $Z_2$-vortex is re-visited in the perspective of harmonic spinors leading to a remarkable result that the gauge potential is exactly the same as the nontrivial harmonic vector field associated with the 2-spinor. It is proposed that a discrete symmetry group $SL(2, Z)$ has a role in connection with the continuous group $SU(2)$ similar to the discrete group $Z_2$ in $U(1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic Spinors and $Z_2$ Vortex Tiwari, S C General Physics Hodge theorem and harmonic spinors are studied in a physics-oriented approach in the present paper. New mathematical results on the harmonic spinors are as follows. Harmonic spinors defined by partial differential operators could be of two types: trivial without topological defects, and having nontrivial topological structures, for example, phase singularities or phase vortices. There could exist a nontrivial harmonic vector field associated with nontrivial harmonic spinor, for example, ${\bf v}_{vortex}$ associated with Weyl 2-spinor. The $Z_2$-vortex is re-visited in the perspective of harmonic spinors leading to a remarkable result that the gauge potential is exactly the same as the nontrivial harmonic vector field associated with the 2-spinor. It is proposed that a discrete symmetry group $SL(2, Z)$ has a role in connection with the continuous group $SU(2)$ similar to the discrete group $Z_2$ in $U(1)$. |
| title | Harmonic Spinors and $Z_2$ Vortex |
| topic | General Physics |
| url | https://arxiv.org/abs/2508.13335 |