In theoretical physics, the ScherkâÂÂSchwarz mechanism (named after Joël Scherk and John Henry Schwarz) for a field àbasically means that àis a section of a non-trivializable fiber bundle (not necessarily a vector bundle since àneedn't be linear) which is fixed by the model. This is called a twist by physicists.
Note that this can never occur in a spacetime which is homeomorphic to R<sup>n</sup>, which is a contractible space. However, for KaluzaâÂÂKlein theories, the ScherkâÂÂSchwarz mechanism is a possibility which can't be neglected.