  We propose an extension of the Schwinger parametric representation for
Feynman amplitudes in $D$ euclidean dimensions to a scenario where $d$
dimensions are compactified ($d<D$) through the introduction of periodic
boundary conditions in space. We obtain two valid representations, one useful
near the bulk (large compactification length) and another useful near the
dimensional reduction (small compactification length). Also, to illustrate, we
exhibit some Feynman amplitudes up to three loops in a compactified scalar
field theory.
