Non-associative slave-boson decomposition

TL;DR

This paper introduces a novel non-associative operator framework to resolve the operator constraint in the t-J model of high-temperature superconductivity, proposing a new algebraic approach for operator decomposition.

Contribution

It presents a new non-associative algebraic method to handle the operator constraint in the t-J model, extending the concept to gluon splitting.

Findings

The operator constraint can be resolved using non-associative operators.

A new algebraic structure is proposed where the constraint acts as an antiassociative generating relation.

The approach suggests a similar constraint for gluon splitting in gauge theories.

Abstract

The operator constraint $f_{i\uparrow}^\dagger f_{i\uparrow} + f_{i\downarrow}^\dagger f_{i\downarrow} + b^\dagger_{i} b_{i}= 1$ 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.