Non-associative slave-boson decomposition

Abstract

An operator constraint for a slave-boson decomposition in t-J model of high temperature superconductivity is considered. It is shown that the constraint can be resolved by introducing a non-associative operator. In this case the constraint is an antiassociative generating relation of a new algebra. Similar constraint is offered for splitting the gluon.2000 MSC: 81Rxx, 17D05