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We apply perturbative renormalization group theory to the symmetric phase ofa dilute interacting Bose gas which is trapped in a three-dimensional harmonicpotential. Using Wilsonian energy-shell renormalization and theepsilon-expansion, we derive the flow equations for the system. We relate theseequations to the flow for the homogeneous Bose gas. In the thermodynamic limit,we apply our results to study the transition temperature as a function of thescattering length. Our results compare well to previous studies of the problem.Comment: 14 pages, 5 figure

Phase transition of trapped interacting Bose gases and the renormalization group