Quantum Hamiltonian reduction of the Schwinger model.

We reexamine a unitary-transformation method of extracting a physical Hamiltonian from a gauge eld theory after quantizing all degrees of freedom including redundant variables. We show that this quantum Hamiltonian reduction method su ers from crucial modi cations arising from regularization of composite operators. We assess the e ects of regularization in the simplest gauge eld theory, the Schwinger model. Without regularization, the quantum reduction yields the identical Hamiltonian with the classically reduced one. On the other hand, with regularization incorporated, the resulting Hamiltonian of the quantum reduction disagrees with that of the classical reduction. However, we nd that the discrepancy is resolved by rede nitions of fermion currents and that the results are again consistent with those of the classical reduction. e-mail address: [email protected]