S. De Bievre
Local states of free bose fields
(570K, postscript)
ABSTRACT. These notes contain an extended version of lectures given at the
``Summer School on Large Coulomb Systems'' in Nordfjordeid,
Norway, in august 2003. They furnish a short introduction to
the theory of quantum harmonic systems, or free bose fields. The main issue addressed is the one of local states. I will adopt the definition of Knight of ``strictly local excitation of the vacuum'' and will then state and prove a generalization of Knight's Theorem which asserts that finite particle states cannot be perfectly localized. It will furthermore be explained
how Knight's a priori counterintuitive result can be readily
understood if one remembers the analogy between finite and
infinite dimensional harmonic systems alluded to above. I will
also discuss the link between the above result and the so-called
Newton-Wigner position operator thereby illuminating, I believe,
the difficulties associated with the latter. I will in particular argue that those difficulties do not find their origin in special relativity or in any form of causality violation, as is usually claimed.