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Free states of the canonical anticommutation relations

Journal:
Communications in Mathematical Physics


Issue Date:
1970


Abstract(summary):

Each gauge invariant generalized free state omega A of the anticommutation relation algebra over a complex Hilbert space K is characterized by an operator A on K. It is shown that the cyclic representations induced by two gauge invariant generalized free states omega A and omega B are quasi-equivalent if and only if the operators A1/2- B1/2 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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