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 ($f_{\alpha }$) and bosonic ($b$) operators. The quantum mechanical constraint $b^{†}b+{\sum }_{\alpha }{f}_{\alpha }^{†}{f}_{\alpha }=1$ 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: $b{b}^{†}b=b$, $f_{\alpha }{f}_{\beta }^{†}{f}_{\gamma }={\delta }_{\alpha \beta }{f}_{\gamma }$ and $f_{\alpha }{b}^{†}=0$. Thereby the algebra of the $X$-operators is preserved exactly 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.

LATEX, 5 pages

References in corpus (1)

• Slave-particle quantization and sum rules in the t-J model