Constraint quantization of slave-particle theories

Abstract

We start from the Barnes-Coleman slave-particle description, where the Hubbard operators X are decomposed into a product of fermionic ( ƒ α ) and bosonic ( b) operators. The quantum mechanical constraint b †b + Σ αƒ α †ƒ α = 1 is treated within the framework of Dirac's method for the quantization of classical constrained systems. This leads to modified algebraic properties of the fundamental operators: bb †b = b, ƒ αƒ β †ƒ γ = δ αβƒ γ and ƒ αb † = 0 . Thereby the algebra of the X-operators is preserved ecactly on the operator level. Matrix representations of the above algebra are constructed and a resolvent-like perturbation theory for the single-impurity Anderson model is developed.