Quantum field theory has been originally conceived to provide a description of
quantum systems consistent with special relativity that allows energy to be converted
into mass (particles). Nowadays, fundamental interactions (except for gravity) are
described in terms of quantum field theory. The attempt made by physicists to connect
the microscopic scale of fundamental interactions with the physics observed at higher
“macroscopic” scales revealed how field theories entail some general concepts
appearing in the description of multiscale phenomena: order/disorder, symmetry
breakdown, collective modes, correlations, macroscopic quantum phenomena just to
mention some of them.
In this course, a brief review of quantum field theories is presented. In particular, it
will be shown how the existence of inequivalent Hilbert space representations in
quantum field theory (a sharp difference to quantum mechanics) provides the natural
conceptual framework to describe multiscale phenomena with applications to
condensed matter physics and biology.
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