Physical Review C

Path integral and boson-fermion expansion in many-fermion systems: Lipkin model

Kazunari Kaneko

Published Nov 1, 1989• 1 citation

Abstract

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.

DOI: 10.1103/physrevc.40.2416

Related papers

Functional integral approach to the Lipkin model

Kazunari Kaneko

A quantum-mechanical formulation involving both collective and independent-particle motions in many-fermion systems is proposed by using the path-integral technique. A semiclassical method of evaluating the functional integral over both fields is described. As an illustration, the Lipkin model is utilized.

Physical Review CJul 1, 19882 citations

Path Integral Approach to Semiclassical Bound State for Many-Fermion Systems: Harmonic Approximation around Static H-F Solutions

Hiroshi Kuratsuji

We give a preliminary report on the bound state quantization of many-fermion systems based on the semiclassical expansion of the path integral in the generalized coherent state representation. As a particular case we consider the quantization around static Hartree-Fock solutions, which reproduces the RPA spectrum such that the correlation energy is naturally included.

Progress of Theoretical PhysicsSep 1, 19830 citations

Path Integral Approach to Many-Body Systems and Classical Quantization of Time-Dependent Mean Field

Hiroshi Kuratsuji, T. Suzuki

We present the path integral formalism of many-body systems based on the representation of generalized coherent states. We give the integral representation for the transition amplitude by utilizing the characteristic property of the coherent states and discuss its classical limit through the method of stationary phase. Applying to the bound state problem, we arrive at the classical quantization rule for the periodic mean field solutions, the utility of which is briefly discussed.

Progress of Theoretical Physics SupplementJan 1, 198322 citations

Utility of Dirac Quantization of Classical System Involving Both Collective and Independent-Particle Degrees of Freedom: A Schematic Model

A. Kuriyama, M. Yamamura

The Dirac quantization method of canonical system with constraints is applied to a classical image of many-fermion system expressed with collective and independent-particle variables. As an illustration, the Lipkin model is adopted. The results are consistent with those coming from the specific properties of the SU(2)-algebra.

Progress of Theoretical PhysicsMar 1, 19814 citations

Fermionic and Bosonic Path Integrals

Lukong Cornelius Fai

This chapter investigates a quantum gas in the grand-canonical ensemble with the grand canonical Hamiltonian ensemble. The path integral formalism pioneered by Feynman has proven to be an extremely useful tool for understanding and handling quantum mechanics, quantum field theory, and statistical mechanics. The path integral approach is a powerful tool that considers nonperturbative calculations for the investigation of many-particle systems. It is worth noting that while the path integral approach seems to be quite cumbersome in quantum mechanics, it does provide a powerful tool in quantum field theory. The entire aforementioned derivation is calculated in order to justify the evaluation of the path integral at equal times. The chapter examines the example of an atomic Fermi gas by considering an electron gas. The Fermi liquid concept is the deviation of the electron gas from the ideal gas behavior. It utilizes the so-called diagram technique to calculate some quantities.

CRC Press eBooksJun 20, 20190 citations

A New Bosonization Procedure of Two-Dimensional Fermion Models in the Path Integral Formulation

J. Sakamoto, a. B. R. Poudel

We present a new bosonization procedure for two-dimensional fermion models in the path integral formulation. We introduce external sources for the fermion currents instead of the auxiliary boson fields used in the conventional procedure. The calculations become much simpler because the external sources do not interact with themselves, while the auxiliary boson fields do, and we can find the equivalent boson models directy. All the formulations are done in Minkowski space-time. The extended Bukhvostov-Lipatov model and the massive Thirring model are discussed here as typical two-dimensional fermion models with current-current-type interactions. The Rothe and Stamatescu model is also discussed, though this is slightly out of the context of bosonization, and the relation of the fermion current in the Heisenberg picture with that in the interaction picture is derived almost straightforwardly. Usually in the operator formalism, this relation is derived using the splitting procedure, which requires detailed calculations. It is expected that we can derive the boson model equivalent to the fermion model with SU(N) symmetry more easily and without any guess work.

Progress of Theoretical PhysicsJul 1, 20004 citations