Abstract
Each gauge invariant generalized free state ω A of the anticommutation relation algebra over a complex Hilbert spaceK is characterized by an operatorA onK. It is shown that the cyclic representations induced by two gauge invariant generalized free states ω A and ω B are quasi-equivalent if and only if the operatorsA 1/2−B 1/2 and (I−A)1/2−(I−B)1/2 are of Hilbert-Schmidt class. The combination of this result with results from the theory of isomorphisms of von Neumann algebras yield necessary and sufficient conditions for the unitary equivalence of the cyclic representations induced by gauge invariant generalized free states.
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Work supported in part by US Atomic Energy Commission, under Contract AT (30-1)-2171 and by the National Science Foundation.
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Powers, R.T., Størmer, E. Free states of the canonical anticommutation relations. Commun.Math. Phys. 16, 1–33 (1970). https://doi.org/10.1007/BF01645492
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DOI: https://doi.org/10.1007/BF01645492