Geometrization of the Lax pair tensors

Download

index.pdf

Date

2000-08-10

Author

Baleanu, D
Baskal, S

Metadata

Show full item record

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

Item Usage Stats

167
views

73
downloads

The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan's torsion tensor. Three-dimensional space-times admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.

Subject Keywords

Physics, mathematical, Astronomy & astrophysics

URI

https://hdl.handle.net/11511/65815

Journal

MODERN PHYSICS LETTERS A

DOI

https://doi.org/10.1142/s0217732300001924

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit Aydogdu, Oktay; Sever, Ramazan (Elsevier BV, 2010-02-01) We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term K. We also investigate the energ...
Scalar waves in a wormhole topology Bugdayci, Necmi (World Scientific Pub Co Pte Lt, 2006-05-01) Global monochromatic solutions of the scalar wave equation axe obtained in flat wormholes of dimensions (2+1) and (3+1). The solutions are in the form of infinite series involving cylindrical and spherical wave functions, and they are elucidated by the multiple scattering method. Explicit solutions for some limiting cases are illustrated as well. The results presented in this work constitute instances of solutions of the scalar wave equation in a space-time admitting closed time-like curves.
Finite action Yang-Mills solutions on the group manifold Dereli, T; Schray, J; Tucker, RW (IOP Publishing, 1996-08-21) We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable solutions of the Yang-Mills equations to be constructed on the group manifold equipped with the natural Cartan-Killing metric. For the unitary unimodular groups the Yang-Mills action integral is finite for such solutions. This is explicitly exhibited for the case of SU(3).
Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential, Wei-Hua Potential, Varshni Potential Arda, Altug; Sever, Ramazan (Walter de Gruyter GmbH, 2014-03-01) Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any K-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n, K).
Interacting quantum topologies and the quantum Hall effect Balachandran, A. P.; Gupta, Kumar S.; Kürkcüoğlu, Seçkin (World Scientific Pub Co Pte Lt, 2008-04-10) 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 coup...

Citation Formats

D. Baleanu and S. Baskal, “Geometrization of the Lax pair tensors,” MODERN PHYSICS LETTERS A, pp. 1503–1510, 2000, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65815.