The symmetries of the Dirac--Pauli equation in two and three dimensions

We calculate all symmetries of the Dirac-Pauli equation in two-dimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of multiple zero modes with their gauge potentials.Comment: 22 pages, Latex. Final version as published in JMP. Contains an additional subsection (4.2) with the explicit construction of multiple zero mode

Conservation laws in Skyrme-type models

The zero curvature representation of Zakharov and Shabat has been generalized recently to higher dimensions and has been used to construct non-linear field theories which either are integrable or contain integrable submodels. The Skyrme model, for instance, contains an integrable subsector with infinitely many conserved currents, and the simplest Skyrmion with baryon number one belongs to this subsector. Here we use a related method, based on the geometry of target space, to construct a whole class of theories which are either integrable or contain integrable subsectors (where integrability means the existence of infinitely many conservation laws). These models have three-dimensional target space, like the Skyrme model, and their infinitely many conserved currents turn out to be Noether currents of the volume-preserving diffeomorphisms on target space. Specifically for the Skyrme model, we find both a weak and a strong integrability condition, where the conserved currents form a subset of the algebra of volume-preserving diffeomorphisms in both cases, but this subset is a subalgebra only for the weak integrable submodel.Comment: Latex file, 22 pages. Two (insignificant) errors in Eqs. 104-106 correcte

Study of the Al-grading effect in the crystallisation of chalcopyrite Cu(In,Al)Se2 thin films selenised at different temperatures

Chalcopyrite CuIn1−xAlxSe2 (CIAS) thin films with an atomic ratio of Al/(In + Al) = 0.4 were grown by a two-stage process onto soda-lime glass substrates. The selenisation was carried out at different temperatures, ranging from 400 °C to 550 °C, for metallic precursors layers evaporated with two different sequences. The first sequence, C1, was evaporated with the Al as the last layer, while in the second one, C2, the In was the last evaporated element. The optical, structural and morphological characterisations led to the conclusion that the precursors sequence determines the crystallisation pathway, resulting in C1 the best option due to the homogeneity of the depth distribution of the elements. The influence of the selenisation temperature was also studied, finding 540 °C as the optimum one, since it allows to achieve the highest band gap value for the C1 sequence and for the given composition

Investigation of the Nicole model

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP^1 Lagrangian density to the non-integer power 3/2 - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behaviour to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemi model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.Comment: Latex, 35 pages, 1 figur

Integrable subsystem of Yang--Mills dilaton theory

With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton. Here integrability means the existence of infinitely many symmetries and infinitely many conserved currents. Further, we construct infinitely many static solutions of this integrable subsystem. These solutions can be identified with certain limiting solutions of the full system, which have been found previously in the context of numerical investigations of the Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the integrable subsystem and show that our static solutions are, in fact, Bogomolny solutions. This explains the linear growth of their energies with the topological charge, which has been observed previously. Finally, we discuss some generalisations.Comment: 25 pages, LaTex. Version 3: appendix added where the equivalence of the field equations for the full model and the submodel is demonstrated; references and some comments adde