arXiv:hep-th/9309028 · Modern Physics Letters A

W∞ COHERENT STATES AND PATH-INTEGRAL DERIVATION OF BOSONIZATION OF NON-RELATIVISTIC FERMIONS IN ONE DIMENSION

Avinash Dhar, Gautam Mandal, Spenta R. Wadia

Published Dec 7, 1993• 36 citations

Abstract

We complete the proof of bosonization of non-interacting non-relativistic fermions in one space dimension by deriving the bosonized action using W∞ coherent states in the fermion path-integral. This action was earlier derived by us using the method of co-adjoint orbits. We also discuss the classical limit of the bosonized theory and indicate the precise nature of the truncation of the full theory that leads to the collective field theory.

DOI: 10.1142/s0217732393002294

Related papers

SEMICLASSICAL APPROACH FOR NONRELATIVISTIC FERMIONS IN LOW DIMENSIONS

Dimitra Karabali A, BUNJI SAKITA

We present a collective field formalism for nonrelativistic fermions in one spatial dimension. A bosonization technique is used to convert the quantum mechanical fermionic problem to a bosonic one, which is further described as a second quantized Schrödinger field theory. A formulation in terms of current and density variables gives rise to the collective field representation. Applications of our formalism to the D=1 Hermitian matrix model and the system of one-dimensional fermions in the presence of a weak electromagnetic field are discussed.

International Journal of Modern Physics ANov 30, 199115 citations

Current Algebra and Bosonization in Three Dimensions

J. C. Le Guillou, Carlos Núñez, F Schaposnik +1 more

We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. We show that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory.

Jan 1, 19960 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

Path integral approach for many-fermion systems and an extension of the time-dependent Hartree-Fock method

Kazunari Kaneko

The quantization of an extended time-dependent Hartree-Fock equation is performed by using the path integral formalism. The path integral form of time evolution operator between initial and final states is obtained with the use of the completeness relation of the fermion coherent states. It is shown that the extended time-dependent Hartree-Fock equation is naturally derived as a classical limit of the path integral.

Physical Review CAug 1, 19846 citations

Fermionic current algebra in three dimensions

Carlos Núñez

We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. It is shown that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory.

AIP conference proceedingsJan 1, 19980 citations

Slave fermions, slave bosons, and semions from bosonization of the two-dimensionalt-Jmodel

Jürg Martin Fröhlich, P. A. Marchetti

We extend Abelian and non-Abelian bosonization formulas found in a previous paper, in combination with coherent-state methods, to present a systematic derivation of the slave-fermion, slave-boson, and semion representations of the two-dimensional t-J model in path-integral form. The slave-fermion and slave-boson representations are shown to arise from two different gauge fixing constraints introduced in the path-integral representation of the bosonized t-J model. For each representation we discuss the approximations leading to a mean-field theory. In the mean-field theory based on the semion representation, the holons are shown to be ``Dirac semions.''

Physical review. B, Condensed matterSep 1, 199245 citations