  We discuss a general class of boundary conditions for bosons living in an
extra spatial dimension compactified on S^1/Z_2. Discontinuities for both
fields and their first derivatives are allowed at the orbifold fixed points. We
analyze examples with free scalar fields and interacting gauge vector bosons,
deriving the mass spectrum, that depends on a combination of the twist and the
jumps. We discuss how the same physical system can be characterized by
different boundary conditions, related by local field redefinitions that turn a
twist into a jump or vice-versa. When the description is in term of
discontinuous fields, appropriate lagrangian terms should be localized at the
orbifold fixed points.
