Geodesic
Statistical nature of Skyrme--Faddeev models in 2+1 dimensions and normalizable fermions
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 3, pp. 381-398

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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, spin statistics, spectral flow.
Mots-clés : skyrmion 
@article{TMF_2019_200_3_a0,
     author = {Yu. Amari and M. Iida and N. Sawado},
     title = {Statistical nature of {Skyrme--Faddeev} models in 2+1 dimensions and normalizable fermions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {381--398},
     publisher = {mathdoc},
     volume = {200},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_3_a0/}
}
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Yu. Amari; M. Iida; N. Sawado. Statistical nature of Skyrme--Faddeev models in 2+1 dimensions and normalizable fermions. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 3, pp. 381-398. http://geodesic.mathdoc.fr/item/TMF_2019_200_3_a0/