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Perturbation theory for the two-dimensional abelian Higgs model in the unitary gauge

In the unitary gauge the unphysical degrees of freedom of spontaneously broken gauge theories are eliminated. The Feynman rules are simpler than in other gauges, but it is non-renormalizable by the rules of power counting. On the other hand, it is formally equal to the limit $ξ\to 0$ of the renormalizable R$_ξ$-gauge. We consider perturbation theory to one-loop order in the R$_ξ$-gauge and in the unitary gauge for the case of the two-dimensional abelian Higgs model. An apparent conflict between the unitary gauge and the limit $ξ\to 0$ of the R$_ξ$-gauge is resolved, and it is demonstrated that results for physical quantities can be obtained in the unitary gauge.