Non-associative slave-boson decomposition

Abstract

The operator constraint $f_{i\uparrow }^{†}{f}_{i\uparrow }+f_{i\downarrow }^{†}{f}_{i\downarrow }+b_i^{†}{b}_i=1$ in t-J model of High-T${}_c$ superconductivity is considered. It is shown that the constraint can be resolved by introdusing 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.

Comments: 5 pages