Free states of the gauge invariant canonical anticommutation relations

Author:
B. M. Baker

Journal:
Trans. Amer. Math. Soc. **237** (1978), 35-61

MSC:
Primary 46L60; Secondary 81E05

MathSciNet review:
479361

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Abstract: The gauge invariant subalgebra of the canonical anticommutation relations (henceforth GICAR) is viewed as an inductive limit of finitedimensional -algebras, and a study is made of a simple class of its representations. In particular, representations induced by restricting the wellknown gauge invariant generalized free states from the entire canonical anticommutation relations (henceforth CAR) are considered. Denoting (a) a state of the CAR by and its restriction to the GICAR by , (b) the unique gauge invariant generalized free state of the CAR such that by , it is shown that induces (an impure) factor representation of the GICAR if and only if , (2) two (impure) GICAR factor representations and are quasi-equivalent if and only if and are Hilbert-Schmidt class operators.

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0479361-6

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

Article copyright:
© Copyright 1978
American Mathematical Society