Quantum corrections to classical confinement

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Abstract
We study two models involving charged scalar fields in one space dimension, which have baglike properties at the classical level. Following conventional renormalization procedures, we find that either the first model becomes a free theory or else its spectrum becomes unbounded below depending on how one renormalizes. The second model also becomes a free theory with a particular choice of renormalization. In no case are we able to retain the classical confinement, although we can restore interactions by adding suitable counterterms to the Hamiltonian.

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