  It has been shown that QED in (1+4)-dimensional space-time, with the fifth
dimension compactified on a circle, leads to CP violation (CPV). Depending on
fermionic boundary conditions, CPV may be either explicit (through the
Scherk--Schwarz mechanism), or spontaneous (via the Hosotani mechanism). The
fifth component of the gauge field acquires (at the one-loop level) a non-zero
vacuum expectation value. In the presence of two fermionic fields, this leads
to spontaneous CPV in the case of CP-symmetric boundary conditions.
Phenomenological consequences are illustrated by a calculation of the electric
dipole moment for the fermionic zero-modes.
