In a previous paper, a quantum-mechanical formulation involving both mean fields and independent-particle fields in many-fermion systems was proposed using the path-integral technique. Then the semiclassical calculation of the energy spectra was performed, and the quantization rule was derived by applying a stationary phase approximation on the path integral. In this paper, a boson-fermion expansion is derived from our formulation using Dirac quantization. As an illustration, the Lipkin model is utilized.In a previous paper, a quantum-mechanical formulation involving both mean fields and independent-particle fields in many-fermion systems was proposed using the path-integral technique. Then the semiclassical calculation of the energy spectra was performed, and the quantization rule was derived by applying a stationary phase approximation on the path integral. In this paper, a boson-fermion expansion is derived from our formulation using Dirac quantization. As an illustration, the Lipkin model is utilized.

Physical Review CNov 1, 19891 citation

Path Integrals for Bosons

Abdulla Rakhimov, Sh. Mardonov

Lecture notes in physicsJan 1, 20260 citations

Asymptotically exact mean-field theory for the Anderson model including double occupancy

J. Holm, Reiner Kree, Kurt Schönhammer

The Anderson impurity model for finite values of the Coulomb repulsion U is studied using a slave-boson representation for the empty and doubly occupied f level. In order to avoid well-known problems with a naive mean-field theory for the boson fields, we use the coherent-state-path integral representation to first integrate out the double-occupancy slave bosons. The resulting effective action is linearized using two-time auxiliary fields. After integration over the fermionic degrees of freedom, one obtains an effective action suitable for a 1/ ${\mathit{N}}_{\mathit{f}}$ expansion. The same problem remains concerning the constraint as in the infinite U case. For T\ensuremath{\rightarrow}0 and ${\mathit{N}}_{\mathit{f}}$ \ensuremath{\rightarrow}\ensuremath{\infty}, exact results for the ground-state properties are recovered in the saddle-point approximation. Numerical solutions of the saddle-point equations show that even in the spin-degenerate case ${\mathit{N}}_{\mathit{f}}$ =2 the results are quite good.The Anderson impurity model for finite values of the Coulomb repulsion U is studied using a slave-boson representation for the empty and doubly occupied f level. In order to avoid well-known problems with a naive mean-field theory for the boson fields, we use the coherent-state-path integral representation to first integrate out the double-occupancy slave bosons. The resulting effective action is linearized using two-time auxiliary fields. After integration over the fermionic degrees of freedom, one obtains an effective action suitable for a 1/${\mathit{N}}_{\mathit{f}}$ expansion. The same problem remains concerning the constraint as in the infinite U case. For T\ensuremath{\rightarrow}0 and ${\mathit{N}}_{\mathit{f}}$\ensuremath{\rightarrow}\ensuremath{\infty}, exact results for the ground-state properties are recovered in the saddle-point approximation. Numerical solutions of the saddle-point equations show that even in the spin-degenerate case ${\mathit{N}}_{\mathit{f}}$=2 the results are quite good.

arXiv:cond-mat/9305028Physical review. B, Condensed matterAug 15, 199313 citations

Path integrals and statistical mechanics

Michael J. Creutz

Cambridge University Press eBooksNov 5, 20220 citations

{\mathit{N}}_{\mathit{f}}

expansion. The same problem remains concerning the constraint as in the infinite U case. For T\ensuremath{\rightarrow}0 and

{\mathit{N}}_{\mathit{f}}

\ensuremath{\rightarrow}\ensuremath{\infty}, exact results for the ground-state properties are recovered in the saddle-point approximation. Numerical solutions of the saddle-point equations show that even in the spin-degenerate case

{\mathit{N}}_{\mathit{f}}

=2 the results are quite good.