Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-10-09
Lect.NotesPhys.718:165-205,2007
Physics
High Energy Physics
High Energy Physics - Theory
Scientific paper
10.1007/3-540-70859-6_7
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.
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