Abstract
It is demonstrated that a field theory of vector mesons interacting with massless fermions in a world of one spatial dimension has an infinite number of solutions in direct analogy to the case of the Thirring model. Each of these solutions corresponds to a different value of a certain parameter ξ which enters into the definition of the current operator of the theory. The physical mass of the vector meson is shown to depend linearly upon this parameter, attaining its bare value μ0 for the exceptional case in which the pseudovector current is exactly conserved. The limits μ02→∞ and μ02→0 are examined; the former yields results previously obtained for the Thirring model while the latter implies a unique value for ξ and defines the radiation gauge formulation of Schwinger’s two-dimensional model of electrodynamics.
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