  We investigate the decoupling of heavy Kaluza-Klein modes in $\phi^{4}$
theory and scalar QED with space-time topology $\mathbb{R}^{3,1} \times S^{1}$.
We calculate the effective action due to integrating out heavy KK modes. We
construct generalized RGE's for the couplings with respect to the
compactification scale $M$. With the solutions to the RGE's we find the
$M$-scale dependence of the effective theory due to higher dimensional quantum
effects. We find that the heavy modes decouple in $\phi^{4}$ theory, but do not
decouple in scalar QED. This is due to the zero mode of the 5-th component
$A_{5}$ of the 5-d gauge field. Because $A_{5}$ is a scalar under 4-d Lorentz
transformations, there is no gauge symmetry protecting it from getting mass and
$A_{5}^{4}$ interaction terms after loop corrections. In light of these
unpleasant features, we explore $S^{1}/\mathbb{Z}_{2}$ compactifications, which
eliminate $A_{5}$, allowing for the heavy modes to decouple at low energies. We
also explore the possibility of decoupling by including higher dimensional
operators. It is found that this is possible, but a high degree of fine tuning
is required.
