  The issue of field redefinition invariance of path integrals in quantum field
theory is reexamined. A ``paradox'' is presented involving the reduction to an
effective quantum-mechanical theory of a $(d+1)$-dimensional free scalar field
in a Minkowskian spacetime with compactified spatial coordinates. The
implementation of field redefinitions both before and after the reduction
suggests that operator-ordering issues in quantum field theory should not be
ignored.
