Abstract
In two-dimensional gauge models the nonintegrable phases of the line Wilson integrals are the only physical gauge field degrees of freedom, providing the gauge field diminishes rather rapidly at spatial infinities. We construct a “physical” quantum Hamiltonian in terms of the physical degrees of freedom for the Schwinger model and the chiral Schwinger model. We show that in the latter case the physical quantum picture can be formulated in two equivalent ways: either in terms of the fermionic matter degrees of freedom moving in a linearly rising background electric field, or in terms of matter fields with exotic statistics.
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