Satoshi Iso

FERMIONS IN THE LOWEST LANDAU LEVEL: Bosonization, W∞ Algebra, Droplets, Chiral Bosons

Abstract We present field theoretical descriptions of massless (2+1) dimensional nonrelativistic fermions in an external magnetic field, in terms of a fermionic and bosonic second quantized language. An infinite dimensional algebra, W∞ appears as the algebra of unitary transformations which preserve the lowest Landau level condition and the particle number. In the droplet approximation it reduces to the algebra of area-preserving diffeomorphisms, which is responsible for the existence of a universal chiral boson lagrangian independent of the electrostatic potential. We argue that the bosonic droplet approximation is the strong magnetic field limit of the fermionic theory. The relation to the c = 1 string model is discussed.

Explicit relation of the quantum Hall effect and the Calogero-Sutherland model

Abstract The explicit relation between the Laughlin state of the quantum Hall effect and the one-dimensional (1D) model with long-ranged interaction (1/ r 2 ) is discussed. By rewriting the lowest Landau level wave functions in terms of the 1D representation, the Laughlin state can be written as a deformation of the ground state of the Calogero-Sutherland model. Corresponding to the Laughlin state on different geometries, different types of 1D 1/ r 2 interaction models are derived.

The massive multi-flavor Schwinger model

Abstract QED with N species of massive fermions on a circle of circumference L is analyzed by bosonization. The problem is reduced to the quantum mechanics of the 2 N fermionic and one gauge field zero modes on the circle, with nontrivial interactions induced by the chiral anomaly and fermions masses. The solution is given for N = 2 and fermion masses ( m ) much smaller than the mass of the U (1) boson with mass μ = 2e 2 π when all fermions satisfy the same boundary conditions. We show that the two limits m → 0 and L → ∞ fail to commute and that the behavior of the theory critically depends on the value of mL| cos 1 2 θ| where θ is the vacuum angle parameter. When the volume is large μL ⪢ 1, fermion condensate 〈 ψ ψ〉 is −(e 4γ mμ 2 cos 4 1 2 θ/4π 3 ) 1 3 or respectively. Its correlation function decays algebraically with a critical exponent η = 1 when m cos 1 2 θ = 0 .

Anyon basis of c = 1 conformal field theory

Abstract We study the c = 1 conformal field theory of a free compactified boson with radius r = √ β (β is an integer). The Fock space of this boson is constructed in terms of chiral “anyon” vertex operators and each state is labeled by an infinite set of pseudo-momenta of filled particles in pseudo-Dirac sea. Wave functions of multi-anyon states are described by eigenfunctions of the Calogero-Sutherland (CS) model. This is a natural generalization of the boson-fermion correspondence in one dimension to the boson-anyon correspondence. There is also an interesting duality between anyons with statistics θ = π / β and particles with statistics θ = βπ .

Collective field theory of the fractional quantum Hall edge state and the Calogero-Sutherland model

Abstract Using the hydrodynamic collective field approximation for the v = 1 m fractional quantum Hall droplet dynamics we find that the low-energy excitations are described by c = 1 conformal field theory of a compact boson of radius √m. Using the conformal field theory method we show that the one-particle density matrix of the edge state interpolates between the chiral Luttinger liquid behavior 〈ψ † (r)ψ(0)〉 ∼ r −m and the Calogero-Sutherland model behavior 〈ψ † (r)ψ(0)〉 ∼ r − ( m+1 m ) 2 as the droplet width is varied continuously. The result suggests complementary relation between the two-dimensional quantum Hall droplet and the one-dimensional Calogero-Sutherland model.

The spin factor in knots and a relativistic treatment of the Bose-Fermi trasmutation in second-quantized theories

Abstract The transmutation of a charged scalar field into a Dirac field is studied. The self-energy of the scalar particle coupled with the Chern-Simons gauge field is evaluated without the loop-splitting regularization. A relation between the spin factor and the self-energy is clarified with the help of a topological feature of a knot. The propagation of a spinning particle in three dimensions is described in terms of the functional integral over random paths with the spin factor. It is shown that the partition function of the charged scalar field is exactly identical with that of a Dirac field in the language of the functional integral.

Geometric description for spinning particles in three dimensions and Chern-Simons-Polyakov theory

Abstract We study the transmutation of a charged scalar particle into a spinning particle. We calculated the propagator for a relativistic particle with a torsion term in three dimensions within the framework of generally covariant field theory in one dimension. It is pointed out that the scalar field is transmuted into the “massive Chern-Simons” field in a particular case.

Interplay between mass, volume, vacuum angle, and chiral condensate in N-flavor two-dimensional QED.

The Schwinger model (QED_2) with N flavors of massive fermions on a circle of circumference L, or equivalently at finite temperature T, is reduced to a quantum mechanical system of N-1 degrees of freedom. With degenerate fermion masses (m) the chiral condensate develops a cusp singularity at

The interplay between mass, volume, \theta, and in N-flavor QED_2

\theta=\pm \pi

THE EFFECT OF DYNAMICAL GAUGE FIELD ON THE CHIRAL FERMION ON A BOUNDARY

in the limit L ->