Topologically Nontrivial Three-Body Contact Interaction in One Dimension
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913201693655040 |
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| author | Ohya, Satoshi |
| author_facet | Ohya, Satoshi |
| contents | It is known that three-body contact interactions in one-dimensional $n(\geq3)$-body problems of nonidentical particles can be topologically nontrivial: they are all classified by unitary irreducible representations of the pure twin group $PT_{n}$. It was, however, unknown how such interactions are described in the Hamiltonian formalism. In this paper, we study topologically nontrivial three-body contact interactions from the viewpoint of the path integral. Focusing on spinless particles, we construct an $n(n-1)(n-2)/3!$-parameter family of $n$-body Hamiltonians that corresponds to one particular one-dimensional unitary representation of $PT_{n}$. These Hamiltonians are written in terms of background Abelian gauge fields that describe infinitely-thin magnetic fluxes in the $n$-body configuration space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16576 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topologically Nontrivial Three-Body Contact Interaction in One Dimension Ohya, Satoshi Quantum Physics High Energy Physics - Theory It is known that three-body contact interactions in one-dimensional $n(\geq3)$-body problems of nonidentical particles can be topologically nontrivial: they are all classified by unitary irreducible representations of the pure twin group $PT_{n}$. It was, however, unknown how such interactions are described in the Hamiltonian formalism. In this paper, we study topologically nontrivial three-body contact interactions from the viewpoint of the path integral. Focusing on spinless particles, we construct an $n(n-1)(n-2)/3!$-parameter family of $n$-body Hamiltonians that corresponds to one particular one-dimensional unitary representation of $PT_{n}$. These Hamiltonians are written in terms of background Abelian gauge fields that describe infinitely-thin magnetic fluxes in the $n$-body configuration space. |
| title | Topologically Nontrivial Three-Body Contact Interaction in One Dimension |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2310.16576 |