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 η-function with a matrix weight. In the presence of such a weight, the usual proof of topological nature of η(0) is not longer applicable. Direct computations confirm the following surprising result: the fermion number induced by vortices in the Jackiw-Rossi model is not topological.