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

Katsunori Kawamura | Zendy

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

Author(s) -

Katsunori Kawamura

Publication year - 2005

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1939989

Subject(s) - fock space , subalgebra , fermion , algebra over a field , boson , current algebra , wedge (geometry) , mathematics , filtered algebra , pure mathematics , physics , quantum mechanics , geometry

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.

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