  In this report I review some aspects of the algebraic structure of QFT
related with the doubling of the degrees of freedom of the system under study.
I show how such a doubling is related to the characterizing feature of QFT
consisting in the existence of infinitely many unitarily inequivalent
representations of the canonical (anti-)commutation relations and how this is
described by the q-deformed Hopf algebra. I consider several examples, such as
the damped harmonic oscillator, the quantum Brownian motion, thermal field
theories, squeezed states, classical-to-quantum relation, and show the
analogies, or links, among them arising from the common algebraic structure of
the q-deformed Hopf algebra.
