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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Free states of the gauge invariant canonical anticommutation relations. II

Author: B. M. Baker
Journal: Trans. Amer. Math. Soc. 254 (1979), 135-155
MSC: Primary 81D05; Secondary 46L10
MathSciNet review: 539911
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Abstract: A class of representations of the gauge invariant subalgebra of the canonical anticommutation relations (henceforth GICAR) is studied. These representations are induced by restricting the well-known pure, nongauge invariant generalized free states of the canonical anticommutation relations (henceforth CAR). Denoting a state of the CAR by $ \omega $, and the unique generalized free state of the CAR such that $ \omega \left( {a{{\left( f \right)}^{\ast}}a\left( g \right)} \right)\, = \,\left( {f,Tg} \right)$ and $ \omega \left( {a\left( f \right)a\left( g \right)} \right)\, = \,\left( {Sf,g} \right)$ by $ {\omega _{S,T}}$, it is shown that a pure, nongauge invariant state $ {\omega _{S,T}}$ induces a factor representation of the GICAR if and only if $ Tr\,T\left( {I - T} \right)\, = \,\infty $.

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PII: S 0002-9947(1979)0539911-9
Keywords: Anticommutation relations, gauge invariance, approximately finite $ {C^{\ast}}$-algebra, generalized free states factor representations
Article copyright: © Copyright 1979 American Mathematical Society

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