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

DOI:
https://doi.org/10.1090/S0002-9947-1979-0539911-9

MathSciNet review:
539911

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Abstract | References | Similar Articles | Additional Information

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 , and the unique generalized free state of the CAR such that and by , it is shown that a pure, nongauge invariant state induces a factor representation of the GICAR if and only if .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0539911-9

Keywords:
Anticommutation relations,
gauge invariance,
approximately finite -algebra,
generalized free states factor representations

Article copyright:
© Copyright 1979
American Mathematical Society