English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

An integrable two-dimensional system related to certain fermion-solitonsystems is studied. The self-consistent solutions of a static version of thesystem are obtained by using the tau function approach. The self-consistentsolutions appear as an infinite number of topological sectors labeled by $n \in\IZ_{+}$, such that in each sector the scalar field would evolve continuouslyfrom a trivial configuration to the one with half integer topological charge.The spinor bound states are found analytically for each topologicalconfiguration of the background scalar field. The bound state energy satisfiesan algebraic equation of degree $2n$, so the study of the energy spectrum findsa connection to the realm of algebraic geometry. We provide explicitcomputations for the topological sectors $n=1,2$. Then, by monitoring theenergy spectrum, including the energy flow of any level across $E_n=0$, wediscuss the vacuum polarization induced by the soliton. It is shown that theequivalence between the Noether and topological currents and the fact that thecoupling constant is related to the one of the Wess-Zumino-Novikov-Witten(WZNW) model imply the quantization of the spinor and topological charges.Moreover, we show that the soliton mass as a function of the boson mass agreeswith the Skyrmes's phenomenological conjecture. Our analytical developmentsimprove and generalize the recent numerical results in the literature performedfor a closely related model by Shahkarami and Gousheh, JHEP06(2011)116. Theconstruction of the bound states corresponding to the topological sectors $n\geq 3$ is briefly outlined.

A fermion-soliton system: self-consistent solutions, vacuum polarization and charge quantization