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This article is cited in 3 scientific papers (total in 3 papers)
Statistical nature of Skyrme–Faddeev models in 2+1 dimensions and normalizable fermions
Yu. Amari, M. Iida, N. Sawado Department of Physics, Tokyo University of Science, Noda, Japan
Abstract:
The Skyrme–Faddeev model has planar soliton solutions with the target space $\mathcal{P}^N$. An Abelian Chern–Simons term (the Hopf term) in the Lagrangian of the model plays a crucial role for the statistical properties of the solutions. Because $\Pi_3(\mathcal{P}^1)=\mathbb{Z}$, the term becomes an integer for $N=1$. On the other hand, for $N>1$, it becomes perturbative because $\Pi_3(\mathcal{P}^N)$ is trivial. The prefactor $\Theta$ of the Hopf term is not quantized, and its value depends on the physical system. We study the spectral flow of normalizable fermions coupled with the baby-Skyrme model $(\mathcal{P}^N$ Skyrme–Faddeev model$)$. We discuss whether the statistical nature of solitons can be explained using their constituents, i.e., quarks.
Keywords:
topological soliton, skyrmion, spin statistics, spectral flow.
Received: 13.12.2018 Revised: 19.02.2019
Citation:
Yu. Amari, M. Iida, N. Sawado, “Statistical nature of Skyrme–Faddeev models in 2+1 dimensions and normalizable fermions”, TMF, 200:3 (2019), 381–398; Theoret. and Math. Phys., 200:3 (2019), 1253–1268
Linking options:
https://www.mathnet.ru/eng/tmf9673https://doi.org/10.4213/tmf9673 https://www.mathnet.ru/eng/tmf/v200/i3/p381
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