  The invariance of physical observables like particle's mass under a local
field redefinition is a well-known and important property of quantum field
theory. In this paper, on the other hand, we investigate nonlocal field
redefinitions eliminating a physical observable from a theory. Indeed, by
giving explicit examples, we present invertible nonlocal field redefinitions
reducing a massive theory to the massless one, and vice versa. The studied
examples are: classical harmonic oscillator, the scalar field theory, and the
Dirac field theory.
