  The canonical operator $\hat{a}^{\dagger}$ ($\hat{a}$) represents the ideal
process of adding (subtracting) an {\it exact} amount of energy $E$ to (from) a
physical system in both elementary quantum mechanics and quantum field theory.
This is a ``sharp'' notion in the sense that no variability around $E$ is
possible at the operator level. In this work, we present a class of deformed
creation and annihilation operators that originates from a rigorous notion of
fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a
simple algebraic structure with modified eigenenergies and Fock states. In
addition, we investigate possible consequences of the introduced formalism in
quantum field theories, as for instance, deviations from linearity in the
dispersion relation for free quasibosons.
