A complete characterization for a general quantum field theory is given of the strictly localized states introduced by J. Knight. It is shown that each such state can be generated from the vacuum by a partially isometric operator. Necessary and sufficient conditions are given for the superposition of such states to be also strictly localized. Finally, it is shown that there is a connection between the von Neumann type of the ring generated by the field operator in a finite region and the possibility of constructing strictly localized states.
REFERENCES
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M. A. Naimark, Normed Rings, translated from the 1st Russian edition by L. F. Boron (P. Noordhoff, Ltd., Groningen, The Netherlands, 1959).
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H. Reeh and S. Schlieder (to be published).
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Reference 3, p. 469, Theorem 2.
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Reference 3, p. 457, Proposition VI.
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Reference 3, p. 465, Eq.
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Reference 3, p. 483, Theorem 2.
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J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer‐Verlag, Berlin, 1932)
[English edition: Princeton University Press, Princeton, New Jersey, 1955].
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© 1963 The American Institute of Physics.
1963
The American Institute of Physics
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