The Quest for Localization

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This talk aims to review the obstacles met in QFT to
reach an appropriate definition for such a basic concept as localization. The
anti-local character of the square root of the "- Laplace-Beltrami +
mass^2" operator prevents the existence of localized states with a finite
number of quanta. (Bosonic) quantum fields describe elementary excitations of
an extended system whose ground state is the vacuum. No wonder, there is a
complicated relationship between the cardinal

(quantal) and continuous (spatial) sides of the theory.
We will also analyze the roles (if any) played in RQI by the localized
excitations of the vacuum.