  A renormalization group theory for a system consisting of coupled
superconducting layers as a model for typical high-temperature superconducters
is developed. In a first step the electromagnetic interaction over infinitely
many layers is taken into account, but the Josephson coupling is neglected. In
this case the corrections to two-dimensional behavior due to the presence of
the other layers are very small. Next, renormalization group equations for a
layered system with very strong Josephson coupling are derived, taking into
account only the smallest possible Josephson vortex loops. The applicability of
these two limiting cases to typical high-temperature superconductors is
discussed. Finally, it is argued that the original renormalization group
approach by Kosterlitz is not applicable to a layered system with intermediate
Josephson coupling.
