arXiv 1210.72332012-10-26hep-thnlin.SI

费米子-孤子系统：自洽解、真空极化和电荷量子化

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

Harold Blas

备注：: 35 pages, 20 figures

摘要：

研究了一类与费米子-孤子系统相关的二维可积系统。利用τ函数方法得到了系统的静态自洽解。自洽解表现为一个由$n \in \IZ_{+}$标记的无穷多个拓扑扇区，使得在每个扇区中的标量场从平凡的组态不断演化到具有半整数拓扑荷的组态.对于背景标量场的每一种拓扑结构，我们都能解析地找到旋量束缚态。束缚态能量满足一个代数方程$2n$，因此能谱的研究与代数几何领域有联系。我们提供了明确的计算拓扑部门$n=1,2$。然后，通过观察能谱，包括任意能级在$E_n=0$上的能流，讨论了孤子引起的真空极化。证明了Noether流与拓扑流的等价性以及Wess-Zumino-Novikov-Witten（WZNW）模型的耦合常数与之相关的事实，暗示了旋量和拓扑荷的量子化.此外，我们表明，孤子质量作为玻色子质量的函数同意Skyrmes的唯象猜想。我们的分析发展改进和推广了Shahkarami和Gousheh，JHEP 06（2011）116中密切相关的模型在文献中进行的最新数值结果。简要介绍了拓扑扇区$n \geq 3$对应的束缚态的构造。

英文摘要：

An integrable two-dimensional system related to certain fermion-soliton systems is studied. The self-consistent solutions of a static version of the system are obtained by using the tau function approach. The self-consistent solutions appear as an infinite number of topological sectors labeled by $n \in \IZ_{+}$, such that in each sector the scalar field would evolve continuously from a trivial configuration to the one with half integer topological charge. The spinor bound states are found analytically for each topological configuration of the background scalar field. The bound state energy satisfies an algebraic equation of degree $2n$, so the study of the energy spectrum finds a connection to the realm of algebraic geometry. We provide explicit computations for the topological sectors $n=1,2$. Then, by monitoring the energy spectrum, including the energy flow of any level across $E_n=0$, we discuss the vacuum polarization induced by the soliton. It is shown that the equivalence between the Noether and topological currents and the fact that the coupling 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 agrees with the Skyrmes's phenomenological conjecture. Our analytical developments improve and generalize the recent numerical results in the literature performed for a closely related model by Shahkarami and Gousheh, JHEP06(2011)116. The construction of the bound states corresponding to the topological sectors $n \geq 3$ is briefly outlined.

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