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The invariance of physical observables like particle's mass under a local field redefinition is a well-known and important property of the quantum field theory. In this letter, 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.
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