Abstract
Several authors have noted an ambiguity with the Dirac equation in one dimension. In the case of a delta-function potential, the coupling constant is subject to an apparently arbitrary renormalization when the delta function is approximated in different ways. We explain these differences in terms of strong resolvent limits of self-adjoint operators onL 2(R), and obtain a precise formula for the renormalized coupling constant in the case of separable potentials. The examples in the literature follow as special cases.
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Research supported in part by a grant from the National Science Foundation.