Recursive Fermion System in Cuntz Algebra. II -- Endomorphism, Automorphism and Branching of Representation --
Recursive Fermion System in Cuntz Algebra. II -- Endomorphism, Automorphism and Branching of Representation --
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Cuntz 代数中的递归费米子系统。
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
Katsunori Kawamura
中科院分区：
文献类型：
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作者：
M. Abe;Katsunori Kawamura
基于CAR代数嵌入到Cuntz代数${\mathcal O}_{2^p}$中的公式，通过限制Cuntz代数的性质，详细研究了CAR代数的性质。明确构造了Cuntz代数的各种$\ast$-自同态，并转录到CAR代数的自同态中。特别地，构造了CAR代数到它的偶子代数的$\ast$-自同态集合。根据组合表示和$\ast$-自同态得到的分支公式，证明了由Fock表示通过上述偶CAR自同态得到CAR代数的KMS状态。$U(2^p)$作用于${\mathcal O}_{2^p}$，得到CAR代数的$\ast$-自同构，这些自同构是由用生成器中的多项式表示的非线性变换给出的。结果表明，在CAR代数的$\ast$-自同构中，存在一类描述费米子时间演化的$\ast$-自同构单参数群，其中系统的粒子数随时间变化，而Fock真空保持不变。
Based 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.
弦论中的伪Cuntz代数和递归费米子系统
DOI：
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发表时间：
2003
期刊：
International Journal of Modern Physics A18
影响因子：
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作者：
Nobuo Inagaki;Yutaka Kano;Nobuo Inagaki;Yutaka Kano;Etuo Kumagai;M.Abe
通讯作者：
M.Abe
CAR费米子代数的非线性变换群
DOI：
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发表时间：
2002
期刊：
Letters in Mathematical Physics 60
影响因子：
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作者：
Nobuo Inagaki;Yutaka Kano;Nobuo Inagaki;Yutaka Kano;Etuo Kumagai;M.Abe;Sigeo Aki;Shigeo Aki;M.Abe;Nobuo Inagaki;M.Abe;白旗 慎吾;M.Abe;M.Abe
通讯作者：
M.Abe