Abstract
Let δ be a quasi-free derivation of the CAR algebra, and let \(\bar \delta \) be a closed *-derivation which is an extension of δ. We use Price's techniques from [6] to show that if the polynomials in the linear field operators a(f)→a * (f) in D(\(\bar \delta \)) is a core for \(\bar \delta \), then \(\bar \delta \) is quasi-free.
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References
ArakiH., Publ. RIMS, Kyoto Univ. 6, 385–442 (1970).
BratteliO. and RobinsonD.W., Operator Algebras and Quantum Statistical Mechanics I, Springer-Verlag, New York, Heidelberg, Berlin, 1979.
BratteliO. and RobinsonD.W., Operator Algebras and Quantum Statistical Mechanics II, Springer-Verlag, New York, Heidelberg, Berlin, 1981.
JørgensenP.E.T., J. Funct. Anal. 45, 341–356 (1982).
McGovernR.J., J. Funct. Anal. 26, 89–101 (1977).
Price, G.L., ‘Extensions of Quasi-free Derivations on the CAR Algebra’, Proc. RIMS Kyoto Univ. (to appear).
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Bratteli, O. A remark on extensions of quasi-free derivations on the CAR-algebra. Lett Math Phys 6, 499–504 (1982). https://doi.org/10.1007/BF00405872
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DOI: https://doi.org/10.1007/BF00405872