Topologically Nontrivial Three-Body Contact Interaction in One Dimension

• URL: http://arxiv.org/abs/2310.16576v2
• Date: Fri, 19 Jan 2024 12:00:00 GMT
• Title: Topologically Nontrivial Three-Body Contact Interaction in One Dimension
• Authors: Satoshi Ohya
• Abstract summary: It is known that three-body contact interactions in one-dimensional $n(geq3)$-body problems of nonidentical particles can be topologically nontrivial. In this paper, we study topologically nontrivial three-body contact interactions from the viewpoint of the path integral.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
  We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions. We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
  arXiv  Detail & Related papers  (2024-07-09T14:04:11Z)
• Helicity is a topological invariant of massless particles: C=-2h [18.79946237767752]
  We show that a subtler relation exists between the topological and geometry of massless particles. We generate all massless bundle representations via an abelian group structure of massless particles.
  arXiv  Detail & Related papers  (2024-07-03T20:48:18Z)
• Hamiltonian for a Bose gas with Contact Interactions [49.1574468325115]
  We study the Hamiltonian for a Bose gas in three dimensions of $N geq 3$ spinless particles interacting via zero-range or contact interactions.
  arXiv  Detail & Related papers  (2024-03-19T10:00:12Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions [77.34726150561087]
  We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
  arXiv  Detail & Related papers  (2022-07-01T10:01:14Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions [68.8204255655161]
  We present a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio model of quantum chromodynamics in 3+1 and 1+1 dimensions. We find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass.
  arXiv  Detail & Related papers  (2020-04-08T14:29:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.