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Conformal scalar fields in curved three-dimensional space

We consider the effect of quantum corrections to a conformally invariant field theory for a scalar field in curved three-dimensional spacetime. In addition to the conformally invariant kinetic action there is a interaction term. The analysis is most easily performed in a space of constant curvature using a formalism of Drummond. Explicit calculation to order shows that all divergences can be removed by renormalizing the cosmological constant and wavefunction; no divergences appear that require the introduction of terms proportionsl to or .