Nonlinear Transformation Group of CAR Fermion Algebra

Abstract

Based on our previous work on the recursive fermion system in the Cuntz algebra, it is shown that a nonlinear transformation group of the CAR fermion algebra is induced from a $U(2^p)$ action on the Cuntz algebra ${\mathcal{O}}_{2^p}$ with an arbitrary positive integer $p$. In general, these nonlinear transformations are expressed in terms of finite polynomials in generators. Some Bogoliubov transformations are involved as special cases.

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• Universal fermionization of bosons on permutative representations of the Cuntz algebra ${\mathcal{O}}_2$
• Nonlinear Bogolyubov-Valatin transformations and quaternions
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