K. Ilyenko | Searcharxiv

arXiv2004

Adjoint representation of the graded Lie algebra osp(2/1; C) and its exponentiation

We construct explicitly the grade star Hermitian adjoint representation of osp(2/1; C) graded Lie algebra. Its proper Lie subalgebra, the even part of the graded Lie algebra osp(2/1; C), is given by su(2) compact Lie algebra. The Baker-Campbell-Hausdorff formula is considered and reality conditions for the Grassman-odd transformation parameters, which multiply the pair of odd generators of the graded Lie algebra, are clarified.

hep-th↗

arXiv2001

Spin Splitting in Quantum Wires with Perturbed Axial Symmetry

We investigate theoretically perturbations to the confining potential capable of lifting spin degeneracy in axially symmetric quasi-one-dimensional electron gases with the spin-orbit interaction. The role of two different types of perturbations breaking axial symmetry of the system: of non-electromagnetic and electromagnetic origin is analyzed. We found that these two types of perturbations have a fundamental distinction in their effects on the energy spectra. The influence of the scale of perturbation upon the value of spin splitting is investigated and it is shown that under certain conditions such splittings can be observed in the experiment.

cond-mat↗