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The induced Chern-Simons term for a paired electron state is calculated inthe quantum Hall system by using a field theory on the von Neumann lattice. Thecoefficient of the Chern-Simons term, which is the Hall conductance, has notonly the usual term proportional to a filling factor due to P (parity) & T(time reversal) symmetry breaking but also correction terms due to P & T & U(1)symmetry breaking. The correction term essentially comes from theNambu-Goldstone mode and depends on an infrared limit. It is shown that thecorrection term is related to a topological number of a gap function in themomentum space.Comment: 26 pages, 6 figure

Induced Chern-Simons term of a paired electron state in the quantum Hall system