Canonical quantization of lattice Chern-Simons theory
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913199380496384 |
|---|---|
| author | Jacobson, Theodore Sulejmanpasic, Tin |
| author_facet | Jacobson, Theodore Sulejmanpasic, Tin |
| contents | We discuss the canonical quantization of $U(1)_k$ Chern-Simons theory on a spatial lattice. In addition to the usual local Gauss law constraints, the physical Hilbert space is defined by 1-form gauge constraints implementing the compactness of the $U(1)$ gauge group, and (depending on the details of the spatial lattice) non-local constraints which project out unframed Wilson loops. Though the ingredients of the lattice model are bosonic, the physical Hilbert space is finite-dimensional, with exactly $k$ ground states on a spatial torus. We quantize both the bosonic (even level) and fermionic (odd level) theories, describing in detail how the latter depends on a choice of spin structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canonical quantization of lattice Chern-Simons theory Jacobson, Theodore Sulejmanpasic, Tin High Energy Physics - Theory High Energy Physics - Lattice We discuss the canonical quantization of $U(1)_k$ Chern-Simons theory on a spatial lattice. In addition to the usual local Gauss law constraints, the physical Hilbert space is defined by 1-form gauge constraints implementing the compactness of the $U(1)$ gauge group, and (depending on the details of the spatial lattice) non-local constraints which project out unframed Wilson loops. Though the ingredients of the lattice model are bosonic, the physical Hilbert space is finite-dimensional, with exactly $k$ ground states on a spatial torus. We quantize both the bosonic (even level) and fermionic (odd level) theories, describing in detail how the latter depends on a choice of spin structure. |
| title | Canonical quantization of lattice Chern-Simons theory |
| topic | High Energy Physics - Theory High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2401.09597 |