Non-topological fractional fermion number in the Jackiw-Rossi model

Abstract

We compute the vacuum fermion current in $(2+1)$ 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 not longer applicable. Direct computations confirm the following surprising result: the fermion number induced by vortices in the Jackiw-Rossi model is \textit{not} topological.

8 pages, revtex

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Cited by in corpus (3)

• Special Functions for Heat Kernel Expansion
• Edge states and the $\eta$ invariant
• Vortex Fractional Fermion Number through Heat Kernel methods and Edge States