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The slave boson method is a technique for dealing with models of strongly correlated systems, providing a method to second-quantize valence fluctuations within a restrictive manifold of states. In the 1960s the physicist John Hubbard introduced an operator, now named the "Hubbard operator" to describe the creation of an electron within a restrictive manifold of valence configurations. Consider for example, a rare earth or actinide ion in which strong Coulomb interactions restrict the charge fluctuations to two valence states, such as the Ce and Ce configurations of a mixed-valence cerium compound. The corresponding quantum states of these two states are the singlet | f 0 ⟩ {\displaystyle \vert f^{0}\rangle } state and the magnetic | f 1 : σ ⟩ {\displaystyle \vert f^{1}:\sigma \rangle } state, where σ =↑ , ↓ {\displaystyle \sigma =\uparrow ,\ \downarrow } is the spin. The fermionic Hubbard operators that link these states are then
The algebra of operators is closed by introducing the two bosonic operators
Together, these operators satisfy the graded Lie algebra
where the ± = A B ± B A {\displaystyle _{\pm }=AB\pm BA} and the sign is chosen to be negative, unless both A {\displaystyle A} and B {\displaystyle B} are fermions, in which case it is positive. The Hubbard operators are the generators of the super group SU. This non-canonical algebra means that these operators do not satisfy a Wick's theorem, which prevents a conventional diagrammatic or field theoretic treatment.