We classify all of the infinitesimal generator extensions of a particular quasi-free derivation δ_A_ on the CAR (canonical anticommutation relations) algebra, where A is an unbounded symmetric operator on a Hilbert space having deficiency indices (1,1). We show that each of these extensions generates a strongly continuous one-parameter group of Bogoliubov transformations of the CAR algebra.
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Geoffrey L. Price, Extensions of Quasi-Free Derivations on the CAR algebra. Publ. Res. Inst. Math. Sci. 19 (1983), no. 1, pp. 345–354DOI 10.2977/PRIMS/1195182992