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Fermions are expressed by polynomials of canonical generators of the Cuntz algebra O2 and they generate the U(1)-fixed point subalgebra A≡O2U(1) of O2 by the canonical gauge action. We extend the Fock and the infinite wedge representations of A to permutative representations of O2. By these extensions, the boson-fermion correspondence is rewritten by canonical generators of O2.

Extensions of representations of the CAR algebra to the Cuntz algebra O2—the Fock and the infinite wedge