Bosonization rules in 12 + 1 dimensions

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its analytic structure.     

Bosonization in higher dimensions via noncommutative field theory

We propose the bosonization of a many-body fermion theory in D spatial dimensions through a noncommutative field theory on a (2D-1)-dimensional space. This theory leads to a chiral current algebra over the noncommutative space and reproduces the correct perturbative Hilbert space and excitation energies for the fermions. The validity of the method is demonstrated by bosonizing a two-dimensional gas of fermions in a harmonic trap.     

Bosonization in (1 + 1) dimensions: An elementary analysis

The expression of a free, massless, Fermi field in terms of scalar field components in a Lorentz basis is obtained. The infrared “disease” of the scalar field is seen to play a positive role in enforcing the fermionic selection rules. Particular attention is paid to the Poincaré transformation properties, both of the Fermi construct and of the Bose constituents. The way that two charge operators are contained in the scalar theory, and the necessary enlargement of the (indefinite metric) space on which the scalar field acts, are discussed in detail.     

Bosonization in curved spacetime

The bosonization of a pair of two-dimensional Weyl fermions, of opposite chiralities, is considered. When the fermions are in different metrics the bosonization procedure gives a unique expression for the gravitational anomaly.     

Bosonization and quantum hydrodynamics

It is shown that it is possible to bosonize fermions in any number of dimensions using the hydrodynamic variables, namely the velocity potential and density. The slow part of the Fermi field is defined irrespective of dimensionality and the commutators of this field with currents and densities are exponentiated using the velocity potential as conjugate to the density. An action in terms of these canonical bosonic variables is proposed that reproduces the correct current and density correlations. This formalism in one dimension is shown to be equivalent to the Tomonaga-Luttinger approach as it leads to the same propagator and exponents. We compute the one-particle properties of a spinless homogeneous Fermi system in two spatial dimensions with long-range gauge interactions and highlight the metal-insulator transition in the system. A general formula for the generating function of density correlations is derived that is valid beyond the random phase approximation. Finally, we write down a formula for the annihilation operator in momentum space directly in terms of number conserving products of Fermi fields.     

A cellular-automaton fluid model with simple rules in arbitrarily many dimensions

A new cellular-automaton model for fluid dynamics is introduced. Unlike the conventional FHP-type models, the model uses easily implementable, deterministic pair interaction rules which work on arbitrary-dimensional orthogonal lattices. The statistical and hydrodynamic theory of the model is developed, and the Navier-Stokes-like hydrodynamic equations that describe the macroscopic behavior of the model are derived. It turns out that the unwanted anisotropic convection behavior can be eliminated in the incompressible limit by suitable choice of the mass density. An explicit expression for the viscosity tensor is calculated from a Boltzmann-type approximation. Unfortunately, the viscosity turns out to be anisotropic, which is a drawback as against the conventional FHP and FCHC models. Nevertheless, the new model could become interesting for fluid dynamic problems with additional variables (e.g., free surfaces), especially in two dimensions, since its simple rules could relatively easily be extended for such cases.     

Bosonization of Massive Fermions

We study the Euclidean sine-Gordon field theory on the plane with β > 16π/3 and an interaction density confined to a finite square. For β= 4 π we construct correlation functions for the field : sin φ \colon; and show that they are equal to the pseudoscalar ―ψΓψ correlation functions for a free fermion theory with mass term confined to the finite square. Received: 19 May 1997 / Accepted: 30 March 1998     

Bosonization of coupled electron-phonon systems

We calculate the single-particle Green’s function of electrons that are coupled to acoustic phonons by means of higher dimensional bosonization. This non-perturbative method is not based on the assumption that the electronic system is a Fermi liquid. For isotropic threedimensional phonons we find that the long-range part of the Coulomb interaction cannot destabilize the Fermi liquid state, although for strong electron-phonon coupling the quasi-particle residue is small. We also show that Luttinger liquid behavior in three dimensions can be due to quasi-one-dimensional anisotropy in the electronic band structure or in the phonon frequencies.     

Bosonization of supersymmetric KdV equation

Bosonization approach to the classical supersymmetric systems is presented. By introducing the multi-fermionic parameters in the expansions of the superfields, the N=1 supersymmetric KdV (sKdV) system is transformed to a system of coupled bosonic equations. The method can be applied to any fermionic systems. By solving the coupled bosonic equations, some novel types of exact solutions can be explicitly obtained. Especially, the richness of the localized excitations of the supersymmetric integrable system is discovered. The rich multi-soliton solutions obtained here have not yet been obtained by using other methods. However, the traditional known multi-soliton solutions can also not be obtained by the bosonization approach of this Letter. Some open problems on the bosonization of the supersymmetric integrable models are proposed in the both classical and quantum levels.     

Bosonization solution of the Falicov-Kimball model

We use a novel approach to analyze the one-dimensional spinless Falicov-Kimball model. We derive a simple effective model for the occupation of the localized orbitals which clearly reveals the origin of the known ordering. Our study is extended to a quantum model with hybridization between the localized and itinerant states: We find a crossover between the well-known weak- and strong-coupling behaviors. The existence of electronic polarons at intermediate coupling is confirmed. A phase diagram is presented and discussed in detail.     

Bosonization for disordered and chaotic systems

Using a supersymmetry formalism, we reduce exactly the problem of electron motion in an external potential to a new supermatrix model valid at all distances. All approximate nonlinear sigma models obtained previously for disordered systems can be derived from our exact model using a coarse-graining procedure. As an example, we consider a model for a smooth disorder and demonstrate that using our approach does not lead to a "mode-locking" problem. As a new application, we consider scattering on strong impurities for which the Born approximation cannot be used. Our method provides a new calculational scheme for disordered and chaotic systems.     

Bosonization and generalized Mandelstam soliton operators

The generalized massive Thirring model (GMT) with three fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with three interacting soliton species. The generalized Mandelstam soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive-definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. In the semi-classical limit one recovers the so-called SU(3) affine Toda model coupled to matter fields (ATM) from which the classical GSG and GMT models were recently derived in the literature. The intermediate ATM-like effective action possesses some spinors resembling the higher grading fields of the ATM theory which have non-zero chirality. These fields are shown to disappear from the physical spectrum, thus providing a bag-model-like confinement mechanism and leading to the appearance of massive fermions (solitons). The ordinary MT/SG duality turns out to be related to each SU(2) sub-group. The higher rank Lie algebra extension is also discussed.Received: 6 July 2004, Published online: 2 September 2004