29 research outputs found
Area Preserving Transformations in Non-commutative Space and NCCS Theory
We propose an heuristic rule for the area transformation on the
non-commutative plane. The non-commutative area preserving transformations are
quantum deformation of the classical symplectic diffeomorphisms. Area
preservation condition is formulated as a field equation in the non-commutative
Chern-Simons gauge theory. The higher dimensional generalization is suggested
and the corresponding algebraic structure - the infinite dimensional -Lie
algebra is extracted. As an illustrative example the second-quantized
formulation for electrons in the lowest Landau level is considered.Comment: revtex, 9 pages, corrected typo
Magnetic Instability in a Parity Invariant 2D Fermion System
We consider the parity invariant (2+1)-dimensional QED where the matter is
represented as a mixture of fermions with opposite spins. It is argued that the
perturbative ground state of the system is unstable with respect to the
formation of magnetized ground state. Carrying out the finite temperature
analysis we show that the magnetic instability disappears in the high
temperature regime.Comment: 7 pages, RevTe
Geometric Transformations and NCCS Theory in the Lowest Landau Level
Chern-Simons type gauge field is generated by the means of the singular area
preserving transformations in the lowest Landau level of electrons forming
fractional quantum Hall state. Dynamics is governed by the system of
constraints which correspond to the Gauss law in the non-commutative
Chern-Simons gauge theory and to the lowest Landau level condition in the
picture of composite fermions. Physically reasonable solution to this
constraints corresponds to the Laughlin state. It is argued that the model
leads to the non-commutative Chern-Simons theory of the QHE and composite
fermions.Comment: Latex, 13 page
Low Energy States in the SU(N) Skyrme Models
We show that any solution of the SU(2) Skyrme model can be used to give a
topologically trivial solution of the SU(4) one. In addition, we extend the
method introduced by Houghton et al. and use harmonic maps from S2 to CP(N-1)
to construct low energy configurations of the SU(N) Skyrme models. We show that
one of such maps gives an exact, topologically trivial, solution of the SU(3)
model. We study various properties of these maps and show that, in general,
their energies are only marginally higher than the energies of the
corresponding SU(2) embeddings. Moreover, we show that the baryon (and energy)
densities of the SU(3) configurations with baryon number B=2-4 are more
symmetrical than their SU(2) analogues. We also present the baryon densities
for the B=5 and B=6 configurations and discuss their symmetries.Comment: latex : 25 pages, 9 Postscript figures, uses eps
The quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice
The tight-binding model of quantum particles on a honeycomb lattice is
investigated in the presence of homogeneous magnetic field. Provided the
magnetic flux per unit hexagon is rational of the elementary flux, the
one-particle Hamiltonian is expressed in terms of the generators of the quantum
group . Employing the functional representation of the quantum group
the Harper equation is rewritten as a systems of two coupled
functional equations in the complex plane. For the special values of
quasi-momentum the entangled system admits solutions in terms of polynomials.
The system is shown to exhibit certain symmetry allowing to resolve the
entanglement, and basic single equation determining the eigenvalues and
eigenstates (polynomials) is obtained. Equations specifying locations of the
roots of polynomials in the complex plane are found. Employing numerical
analysis the roots of polynomials corresponding to different eigenstates are
solved out and the diagrams exhibiting the ordered structure of one-particle
eigenstates are depicted.Comment: 11 pages, 4 figure