Hopf Term for a Two-Dimensional Electron Gas

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In this Comment on the paper by W. Apel and Yu. A. Bychkov, cond-mat/9610040 and Phys. Rev. Lett. 78, 2188 (1997), we draw attention to our prior microscopic derivations of the Hopf term for various systems and to shortcomings of the Apel-Bychkov derivation. We explain how the value of the Hopt term prefactor Θ is expressed in terms of a topological invariant in the momentum space and the quantized Hall conductivity of the system. (See also related paper cond-mat/9703195)