Quantum Hamiltonian Reduction of the Schwinger Model

Details Quantum Hamiltonian Reduction of the Schwinger Model Quantum Hamiltonian Reduction of the Schwinger Model

1994-06-29

arxiv.org/abs/hep-th/9406195v1

Phys.Rev. D50 (1994) 4145-4156

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, LaTeX file, UT-Komaba 94-5

Scientific paper

10.1103/PhysRevD.50.4145

We reexamine a unitary-transformation method of extracting a physical Hamiltonian from a gauge field theory after quantizing all degrees of freedom including redundant variables. We show that this {\it quantum Hamiltonian reduction} method suffers from crucial modifications arising from regularization of composite operators. We assess the effects of regularization in the simplest gauge field 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 find that the discrepancy is resolved by redefinitions of fermion currents and that the results are again consistent with those of the classical reduction.

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