Hopf maps as static solutions of the complex eikonal equation

We demonstrate that a class of torus-shaped Hopf maps with arbitrary linking number obeys the static complex eikonal equation. Further, we explore the geometric structure behind these solutions, explaining thereby the reason for their existence. As this equation shows up as an integrability condition in certain non-linear field theories, the existence of such solutions is of some interest.Comment: 13 pages, slight changes in presentation, one paragraph on the symmetries of the eikonal equation added. Version accepted for publication in JM

Dynamical chiral symmetry breaking with Minkowski space integral representations

The fermion propagator is studied in the whole Minkowski space with the help of the Schwinger-Dyson equations. Various integral representations are employed to get solutions for the dynamical breaking of chiral symmetry in different regimes of the coupling constant. In particular, in the case of massive boson, we extend the singularity structure of the fermion propagator to the two real pole Ansatz.Comment: 4 pages, 4 figures, published version in PR

Anisotropy of photon production: Initial eccentricity or magnetic field

Recent measurements of the azimuthal anisotropy of direct photons in heavy-ion collisions at the energies of RHIC show that it is of the same order as the hadronic one. This finding appears to contradict the expected dominance of photon production from a quark-gluon plasma at an early stage of a heavy-ion collision. A possible explanation of the strong azimuthal anisotropy of the photons, given recently, is based on the presence of a large magnetic field in the early phase of a collision. In this letter, we propose a method to experimentally measure the degree to which a magnetic field in heavy-ion collisions is responsible for the observed anisotropy of photon production. The experimental test proposed in this letter may potentially change our understanding of the non-equilibrium stage and possible thermalization in heavy-ion collisions.Comment: 4 pages, 3 figures; version accepted for publication: discussions extended, MC calculations adde

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