Recursive Fermion System in Cuntz Algebra. II -- Endomorphism, Automorphism and Branching of Representation --

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dc.creatorAbe, Mitsuo
dc.creatorKawamura, Katsunori
dc.date2002-07-01
dc.date.accessioned2026-07-07T04:29:17Z
dc.date.available2026-07-07T04:29:17Z
dc.descriptionBased on an embedding formula of the CAR algebra into the Cuntz algebra ${\mathcal O}_{2^p}$, properties of the CAR algebra are studied in detail by restricting those of the Cuntz algebra. Various $\ast$-endomorphisms of the Cuntz algebra are explicitly constructed, and transcribed into those of the CAR algebra. In particular, a set of $\ast$-endomorphisms of the CAR algebra into its even subalgebra are constructed. According to branching formulae, which are obtained by composing representations and $\ast$-endomorphisms, it is shown that a KMS state of the CAR algebra is obtained through the above even-CAR endomorphisms from the Fock representation. A $U(2^p)$ action on ${\mathcal O}_{2^p}$ induces $\ast$-automorphisms of the CAR algebra, which are given by nonlinear transformations expressed in terms of polynomials in generators. It is shown that, among such $\ast$-automorphisms of the CAR algebra, there exists a family of one-parameter groups of $\ast$-automorphisms describing time evolutions of fermions, in which the particle number of the system changes by time while the Fock vacuum is kept invariant.
dc.description47 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math-ph/0207003
dc.identifierhttp://arxiv.org/abs/math-ph/0207003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57098
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectOperator Algebras
dc.subject81R15; 46L40
dc.titleRecursive Fermion System in Cuntz Algebra. II -- Endomorphism, Automorphism and Branching of Representation --
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