Abstract
The concept of the loop group describes a conformal model in terms of bounded operators. The simplest possibility, the central extended U(1) loop group algebra spanned by operators W(f), f:S{sup 1}{yields}R satisfying Weyl algebra relations is considered. The possibility that the loop group element e{sup if} represented by W(f) does not necessarily lie in the identity component is investigated. This leads to a quantization of the level parameter k in the cocycle. Considering this `large` loop group algebra as the algebra of observables, their Z{sub k} type of superselection sectors is studied, and fields are constructed that create the Z{sub k} charges. The commutation relations of these fields turn out to be of the parafermion type. (K.A.) 4 refs.
Citation Formats
Boehm, G, and Szlachanyi, K.
Z(2N) parafermions from U(1) loop group.
Hungary: N. p.,
1993.
Web.
Boehm, G, & Szlachanyi, K.
Z(2N) parafermions from U(1) loop group.
Hungary.
Boehm, G, and Szlachanyi, K.
1993.
"Z(2N) parafermions from U(1) loop group."
Hungary.
@misc{etde_10113692,
title = {Z(2N) parafermions from U(1) loop group}
author = {Boehm, G, and Szlachanyi, K}
abstractNote = {The concept of the loop group describes a conformal model in terms of bounded operators. The simplest possibility, the central extended U(1) loop group algebra spanned by operators W(f), f:S{sup 1}{yields}R satisfying Weyl algebra relations is considered. The possibility that the loop group element e{sup if} represented by W(f) does not necessarily lie in the identity component is investigated. This leads to a quantization of the level parameter k in the cocycle. Considering this `large` loop group algebra as the algebra of observables, their Z{sub k} type of superselection sectors is studied, and fields are constructed that create the Z{sub k} charges. The commutation relations of these fields turn out to be of the parafermion type. (K.A.) 4 refs.}
place = {Hungary}
year = {1993}
month = {Apr}
}
title = {Z(2N) parafermions from U(1) loop group}
author = {Boehm, G, and Szlachanyi, K}
abstractNote = {The concept of the loop group describes a conformal model in terms of bounded operators. The simplest possibility, the central extended U(1) loop group algebra spanned by operators W(f), f:S{sup 1}{yields}R satisfying Weyl algebra relations is considered. The possibility that the loop group element e{sup if} represented by W(f) does not necessarily lie in the identity component is investigated. This leads to a quantization of the level parameter k in the cocycle. Considering this `large` loop group algebra as the algebra of observables, their Z{sub k} type of superselection sectors is studied, and fields are constructed that create the Z{sub k} charges. The commutation relations of these fields turn out to be of the parafermion type. (K.A.) 4 refs.}
place = {Hungary}
year = {1993}
month = {Apr}
}