Topologically Nontrivial Three-Body Contact Interaction in One Dimension

Autor:	Ohya, Satoshi
Rok vydání:	2023
Předmět:	Quantum Physics High Energy Physics - Theory
Zdroj:	Prog.Theor.Exp.Phys.2024:013A01,2024
Druh dokumentu:	Working Paper
DOI:	10.1093/ptep/ptad149
Popis:	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. Comment: 12 pages, many tikz figures; typos corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.16576 Zobrazit plný text záznamu View this record from Arxiv