We compute the vacuum fermion current in the ($2+1$) dimensional Jackiw-Rossi model by using the $1/m$ expansion. The current is expressed through a weighted $\eta$-function with a matrix weight. In the presence of such a weight, the usual proof of topological nature of $\eta (0)$ is no longer applicable. Direct computations confirm the following surprising result; the fermion number induced by vortices in the Jackiw-Rossi model is not topological.

中文翻译：

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Jackiw-Rossi 模型中的非拓扑分数费米子数

我们计算真空费米子电流 ($2+1$) 维 Jackiw-Rossi 模型通过使用 $1/米$扩张。电流通过加权表示$\eta$- 具有矩阵权重的函数。在存在这样的权重的情况下，拓扑性质的通常证明$\eta (0)$不再适用。直接计算证实了以下令人惊讶的结果；Jackiw-Rossi 模型中由涡流引起的费米子数不是拓扑的。