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Structures of spinors fiber bundles with special relativity of Dirac operator using the Clifford algebra

Hassan Yousif Atyeib Ibrahim

Demonstratio Mathematica

2021

Vol. 54, nr 1

410--424

The purpose of this article is to demonstrate how to use the mathematics of spinor bundles and their category. We have used the methods of principle fiber bundles obey thorough solid harmonic treatment of pseudo-Riemannian manifolds and spinor structures with Clifford algebras, which couple with Dirac operator to study important applications in cohomology theory.

Inhomogeneous superconductivity and vortices in the stripe states

Lenkowska-Czerwińska T.

Journal of Technical Physics

2002

Vol. 43, no 3

335-341

Spatially inhomogeneous features in the spin and charge structures have been indicated in the number of experiments on high temperature materials e.g. La2-xSrxCuO4. The simple realization of this state is striped domain wall where charges form a nanoscale linear pattern in an antiferromagnetically ordered isolator. These represent a nanoscale distribution of charge and spin that is believed to be commensurably locked by the tilt distortions of the lattice. The phenomenological model of charge and spin inhomogeneities in the stripe phase of superconducting cuprates on the ground of Ginzburg-Landau theory is proposed. The corresponding free energy for the coupled charge and spin-density wave, and superconducting order parameters is constructed. The phase diagram for inhomogeneous superconducting state is discussed. The effective coherence length and the penetration depth in the London limit are introduced. The critical magnetic fields and the energy of the isolated vortex line are obtained.