Induced Charge in 2+1 Dimensions

Induced Charge is investigated for a massive fermion system under atime-dependent external potential in 2+1 dimensions. First a clear definitionof Induced Charge is given and then we prove that, under a certain condition(H-S), a concrete procedure is given to derive an explicit formula toevaluate Induced Charge. Using our formula we can show analytically thatInduced Charge is equal to the number of the levels that cross zero due tothe change of the external potential. Finally one of the non trivial examplesis presented for the systems which develop non-zero integer Induced Charge.