Abstract
Within the context of a bosonized theory, we evaluate the current-current correlation functions corresponding to a massive Dirac field in 2+1 dimensions, which is constrained to a spatial half-plane. The boundary conditions are imposed on the dual theory, and have the form of of perfect-conductor conditions. We also consider, for the sake of comparison, the purely fermionic version of the model and its boundary conditions, in the large-mass limit. We apply the result about the dual theory to the evaluation of induced vacuum currents in the presence of an external field, in a spatial half-plane.
Highlights
For a massive Dirac field in 2+1 dimensions, the situation we are concerned with here, the path integral bosonization framework may be used to derive the exact bosonization rule for the current
Within the context of a bosonized theory, we evaluate the current-current correlation functions corresponding to a massive Dirac field in 2 + 1 dimensions, which is constrained to a spatial half-plane
In a previous work [7], we have applied the functional bosonization approach to a system consisting of a massive Dirac field constrained to a 2+1 dimensional spacetime manifold U, with non-trivial conditions on its boundary M ≡ ∂U
Summary
For a massive Dirac field in 2+1 dimensions, the situation we are concerned with here, the path integral bosonization framework may be used to derive the exact bosonization rule for the current. In a previous work [7], we have applied the functional bosonization approach to a system consisting of a massive Dirac field constrained to a 2+1 dimensional spacetime manifold U, with non-trivial conditions on its boundary M ≡ ∂U.
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