2,425 research outputs found
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
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