Dimensional Boson Research Articles

Topological equivalence in the theory of trapped ions

We consider an ion whose motion is confined to a plane perpendicular to a constant magnetic field. A harmonic trapping field is applied within the plane of the ion's motion, together with some unspecified irradiating probe beam. By determining the dynamics of the ion we show that the particle theory is formally equivalent to that of a coupled massive (1 + 2)-dimensional vector Boson field. The field characteristics of current and Proca mass take on the roles of the interaction and harmonic potential respectively of the ion. The topological mass appropriate to the restricted configuration space, which in the case of the vector Boson field is given by the Chern-Simons term, is provided by the constant magnetic field.

Edge theory of ferromagnetic quantum Hall states

We propose an effective low-energy theory for ferromagnetic Hall states. It describes the charge degrees of freedom, on the edge, by a $(1\phantom{\rule{0ex}{0ex}}+\phantom{\rule{0ex}{0ex}}1)$ dimensional chiral boson theory, and the spin degrees of freedom by the $(2\phantom{\rule{0ex}{0ex}}+\phantom{\rule{0ex}{0ex}}1)$ dimensional quantum ferromagnet theory in the spin-wave approximation. The usual chiral boson theory for spinless electrons is modified to include the charge degrees of freedom with spin. Our total, bulk plus edge, effective action is gauge invariant and we find a generalized ``chiral anomaly'' in this case. We describe two, charged and neutral, sets of edge spin-wave solutions. The spreading of these waves is much larger than the one for the charge (edge) waves and they have linear dispersion relations.

On three dimensional bosonization

We discuss Abelian and non-Abelian three dimensional bosonization within the path-integral framework. We present a systematic approach leading to the construction of the bosonic action which, together with the bosonization recipe for fermion currents, describes the original fermion system in terms of vector bosons.

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 {\it{not}} based on the assumption that the electronic system is a Fermi liquid. For isotropic three-dimensional 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 {\it{or in the phonon frequencies}}.

Geometrical approach to bosonization of D>1 dimensional (non)-Fermi liquids.

We discuss an approach to higher dimensional bosonization of interacting fermion s based on a picture of fluctuating Fermi surface. Compared with the linearized"constructive" approach developed in Refs.[9-11] this method allows an account of the Fermi surface curvature due to nongaussian terms in the bosonized Lagrangian. On the basis of this description we propose a procedure of calculating density response functions beyond the random phase approximation. We also formulate a bosonic theory of the compressible metal-like state at half filled lowest Landau level and check that in gaussian approximation it reproduces RPA results of the gauge theory by Halperin, Lee, and Read.

Trivedi and Makivic Reply

In response to a recent comment [Phys. Rev. Lett. 74 1038 (1995)], the authors further their Monte Carlo study of the two[minus]dimensional dirty boson problem. (AIP)

Study on the one dimensional boson–fermion model

The one dimensional boson–fermion model is introduced and the general eigenstates of the model Hamiltonian are constructed. The Cooper-pairlike bound state is given. It is concluded that the present model is exactly soluble via the Bethe ansatz.

Smooth bosonization. The massive case

The (1 + 1)-dimensional bosonization relations for fermionic mass termsare derived by choosing a specific gauge in an enlarged gauge-invariant theory containing both fermionic and bosonic fields. The fermionic part of the generating functional subject to the gauge constraint can be cast into the form of a strongly coupled Schwinger model, which can be solved exactly. The resulting bosonic theory coupled to the scalar sources then exhibits directly the bosonic counterparts of the fermionic densities ψψ and ψγ 5ψ .

Canonical quantization of theories containing fractional powers of the d'Alembertian operator

The authors present a canonical formulation for theories whose actions contain noninteger powers of the d'Alembertian operator and which were recently shown to play a central role in (2+1)-dimensional bosonization. They show that these theories possess an infinite number of constraints and use the Dirac method in order to obtain the classical brackets. The causal and classical Green functions are obtained and their meaning in terms of field expectation values is discussed. The Wightman functions are introduced and shown to lead to the microcausality principle. A mode expansion for the field is obtained. This permits the re-obtainment of the Wightman functions as vacuum expectation values of products of the basic fields. Creation and annihilation operators are naturally introduced but, as shown, they are not related to definite mass particle states. This is also confirmed by the spectral decomposition of the Wightman functions.

Charged boson condensation in high-Tc superconductors.

We explore the superconducting transiton in the RVB (resonant valence bond) model, assuming that the superconductivity is due to a Bose-Einstein condensation of charged bosons in the RVB vacuum. It appears that the charged bosons behave like a weakly interacting 2+epsilon dimensional boson gas and that the RVB superconductors exhibit many two-dimensional properties. Among others are a linear temperature dependence of the critical fields, which has already been observed in experiments, and a linear doping dependence of the transition temperature.

Bounds on the coupling constant in two dimensional boson models

We consider two dimensional boson field theories with an interaction potentialV (φ). We show how to define a cut-off, renormalised Hamiltonian for a certain class of non-polynomialV (φ), which are defined via an integral transform. We formulate precisely a variational argument devised by Coleman, obtaining a constraint on the coupling constant of the theory with generalV (φ), and illustrate the argument with several examples.