Interacting quantum topologies and the quantum Hall effect

Download

index.pdf

Date

2008-04-10

Author

Balachandran, A. P.
Gupta, Kumar S.
Kürkcüoğlu, Seçkin

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

215
views

75
downloads

The algebra of observables of planar electrons subject to a constant background magnetic field B is given by A(theta)(R-2) circle times A(theta)(R-2) (theta = -4/eB), the product of two mutually commuting Moyal algebras. It describes the free Hamiltonian and the guiding center coordinates. We argue that A(theta)(R-2) itself furnishes a representation space for the actions of these two Moyal algebras, and suggest physical arguments for this choice of the representation space. We give the proper setup to couple the matter fields based on A(theta)(R-2) to electromagnetic fields which are described by the Abelian commutative gauge group G(c)(U(1)), i.e. gauge fields based on A(0)(R-2). This enables us to give a manifestly gauge covariant formulation of integer quantum Hall effect (IQHE). Thus, we can view IQHE as an elementary example of interacting quantum topologies, where matter and gauge fields based on algebras A(theta)' with different theta' appear. Two-particle wave functions in this approach are based on A(theta)(R-2) circle times A(theta)(R-2). We find that the full symmetry group in IQHE, which is the semidirect product SO(2) x G(c)(U(1)) acts on this tensor product using the twisted coproduct Delta(theta). Consequently, as we show, many particle sectors of each Landau level have twisted statistics. As an example, we find the twisted two particle Laughlin wave functions.

Subject Keywords

Nuclear and High Energy Physics, Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

URI

https://hdl.handle.net/11511/45767

Journal

INTERNATIONAL JOURNAL OF MODERN PHYSICS A

DOI

https://doi.org/10.1142/s0217751x08039888

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

Mass spectra of heavy quarkonia and B-c decay constant for static scalar-vector interactions with relativistic kinematics Ikhdair, SM; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2005-11-10) We reproduce masses of the self-conjugate and non-self-conjugate mesons in the context of the spinless Salpeter equation taking into account the relativistic kinematics and the quark spins. The hyperfine splittings for the 2S charmonium and IS bottomonium are also calculated. Further, the pseudoscalar and vector decay constants of the Be meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of t...
HIGHER-DERIVATIVE EFFECTIVE YANG-MILLS THEORY AND STATIC SPHERICALLY SYMMETRICAL FIELD CONFIGURATIONS BASKAL, S; DERELI, T (IOP Publishing, 1993-04-01) The variational field equations and the covariantly conserved energy-momentum tensor of a higher-derivative effective Yang-Mills theory are given. A class of static spherically symmetric gauge field configurations that follow from the Wu-Yang ansatz is considered.
Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01) Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...
Pseudospin and spin symmetry in Dirac-Morse problem with a tensor potential AYDOĞDU, OKTAY; Sever, Ramazan (Elsevier BV, 2011-09-14) Under the conditions of the pseudospin and spin symmetry, approximate analytical solutions of the Dirac-Morse problem with Coulomb-like tensor potential are presented. The energy eigenvalue equations are found and corresponding radial wave functions are obtained in terms of confluent hypergeometric functions. The energy eigenvalues are calculated numerically in the absence and presence of the tensor potential. We also investigate the contribution of the potential parameters to the energy splitting of the ps...
CORE POLARIZATION EFFECTS ON THE MAGNETIC FORM-FACTORS OF N-15 AND O-17 GOKALP, A; YILMAZ, O (Springer Science and Business Media LLC, 1992-05-01) The effects of the first- and the second-order core polarization on the elastic magnetic form factors of N-15 and O-17 are investigated using the perturbation theory based on the harmonic-oscillator shell model, in which for the matrix elements of the two-nucleon interaction the Sussex matrix elements are employed. The core polarization reduces the single-particle value of M3 part of the form factor of O-17, however the reduction of the form factor of N-15 does not lead to an improved agreement with experim...

Citation Formats

A. P. Balachandran, K. S. Gupta, and S. Kürkcüoğlu, “Interacting quantum topologies and the quantum Hall effect,” INTERNATIONAL JOURNAL OF MODERN PHYSICS A, pp. 1327–1336, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45767.