Abstract
We solve the N-body Calogero problem, i.e., N particles in one dimension subject to a two-body interaction of the form 1/2 {Sigma}{sub i,j} ((x{sub i}-x{sub j}){sup 2}+g/(x{sub i}-x{sub j}){sup 2}), by constructing annihilation and creation operators of the form a{sub i}{sup -+}=(1/{radical}2)(x{sub i}{+-}ip{sub i}) where p{sub i} is a modified momentum operator obeying Heisenberg-type commutation relations with x{sub i}, involving explicitly permutation operators. On the other hand, D{sub j}=ip{sub j} can be interpreted as a covariant derivative corresponding to a flat connection. The relation to fractional statistics in 1+1 dimensions and anyons in a strong magnetic field is briefly discussed. (orig.).
Brink, L;
[1]
Hansson, T H;
[2]
Vasiliev, M A
[3]
- Inst. of Theoretical Physics, CTH, Goeteborg (Sweden)
- Inst. of Theoretical Physics, Univ. Stockholm (Sweden)
- Dept. of Theoretical Physics, P.N. Lebedev Physical Inst., Moscow (Russia)
Citation Formats
Brink, L, Hansson, T H, and Vasiliev, M A.
Explicit solution to the N-body Calogero problem.
Netherlands: N. p.,
1992.
Web.
doi:10.1016/0370-2693(92)90166-2.
Brink, L, Hansson, T H, & Vasiliev, M A.
Explicit solution to the N-body Calogero problem.
Netherlands.
https://doi.org/10.1016/0370-2693(92)90166-2
Brink, L, Hansson, T H, and Vasiliev, M A.
1992.
"Explicit solution to the N-body Calogero problem."
Netherlands.
https://doi.org/10.1016/0370-2693(92)90166-2.
@misc{etde_7003570,
title = {Explicit solution to the N-body Calogero problem}
author = {Brink, L, Hansson, T H, and Vasiliev, M A}
abstractNote = {We solve the N-body Calogero problem, i.e., N particles in one dimension subject to a two-body interaction of the form 1/2 {Sigma}{sub i,j} ((x{sub i}-x{sub j}){sup 2}+g/(x{sub i}-x{sub j}){sup 2}), by constructing annihilation and creation operators of the form a{sub i}{sup -+}=(1/{radical}2)(x{sub i}{+-}ip{sub i}) where p{sub i} is a modified momentum operator obeying Heisenberg-type commutation relations with x{sub i}, involving explicitly permutation operators. On the other hand, D{sub j}=ip{sub j} can be interpreted as a covariant derivative corresponding to a flat connection. The relation to fractional statistics in 1+1 dimensions and anyons in a strong magnetic field is briefly discussed. (orig.).}
doi = {10.1016/0370-2693(92)90166-2}
journal = []
volume = {286:1/2}
journal type = {AC}
place = {Netherlands}
year = {1992}
month = {Jul}
}
title = {Explicit solution to the N-body Calogero problem}
author = {Brink, L, Hansson, T H, and Vasiliev, M A}
abstractNote = {We solve the N-body Calogero problem, i.e., N particles in one dimension subject to a two-body interaction of the form 1/2 {Sigma}{sub i,j} ((x{sub i}-x{sub j}){sup 2}+g/(x{sub i}-x{sub j}){sup 2}), by constructing annihilation and creation operators of the form a{sub i}{sup -+}=(1/{radical}2)(x{sub i}{+-}ip{sub i}) where p{sub i} is a modified momentum operator obeying Heisenberg-type commutation relations with x{sub i}, involving explicitly permutation operators. On the other hand, D{sub j}=ip{sub j} can be interpreted as a covariant derivative corresponding to a flat connection. The relation to fractional statistics in 1+1 dimensions and anyons in a strong magnetic field is briefly discussed. (orig.).}
doi = {10.1016/0370-2693(92)90166-2}
journal = []
volume = {286:1/2}
journal type = {AC}
place = {Netherlands}
year = {1992}
month = {Jul}
}