Free states of the gauge invariant canonical anticommutation relations
Author:
B. M. Baker
Journal:
Trans. Amer. Math. Soc. 237 (1978), 3561
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 quasiequivalent if and only if and are HilbertSchmidt class operators.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197804793616
PII:
S 00029947(1978)04793616
Keywords:
Anticommutation relations,
gauge invariance,
approximately finite algebra,
generalized free states,
factor representations,
quasiequivalent representations
Article copyright:
© Copyright 1978
American Mathematical Society
