权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Operator Formalism of Quantum Field Theory and Operator Algebra

量子场论和算子代数的算子形式主义

基本信息

批准号：
14540112
负责人：
ABE Mitsuo
金额：
$ 2.56万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540112/
关键词：
Quantum Field Theory Operator Formalism Exact Solution Anomaly Operator Algebra Cuntz Algebra CAR Algebra Embedding 量子重力重力アノマリー T^*積場の方程式無限次元対称性 Noetherの定理フェルミオン自己準同型自己同型 KMS状態

项目摘要

The structure of the CAR algebra describing a fermion system is clarified through a new approach using restrictions of the Cuntz algebra. First, embeddings, automorphisms, endomorphisms, and various representations of Cuntz algebras are explicitly constructed. Second, by restricting them to the embedded CAR algebra in the Cuntz algebra, the corresponding structures of the CAR algebra are obtained. Using a certain class of endomorphorphisms, it is shown that the KMS states as the mixed states of a fermion system are obtained from the Fock representation as the pure state. This result corresponds to the theory of Araki-Woods factors in the classification of von Neumann algebras. By restricting automorphisms, various nontrivial time evolutions of a fermion system are explicitly constructed, which give new constructions of solvable fermion systems. As for the indefinite-metric fermion system in gauge theories, the pseudo Cuntz algebra plays the similar role as above. Therefore, the problem … More of representation of the FP ghosts in string theory is clarified likewise.It is shown that the existence of the gravitational anomaly in two dimensions cannot be established by the reasoning of Alvarez-Gaume and Witten. Its drawback is the confusion of the T^*-product quantities with the T-product ones. In contrast with the T-product, the T^*-product commutes with the time differentiation, however some field equations are apparently broken. This problem has nothing to do with anomaly. The result obtaied by Alvarez-Gaume and Witten is shown to be quantitatively the same as the apparent breakdown of the field equation in the T^*-product.As concerns the solvability of the conformal-gauge two-dimensional quantum gravity, constructions of the infinite-dimensional symmetry corresponding to the infinite-number of conserved quantities are studied. Owing to the speciality of the field equation as the conformal-gauge condition, it is difficult to define the symmetry transformation of fields from a generic conserved quantitity as a symmetry generator. This procedure corresponds to the inverse problem of the Noether theorem. Less

利用Cuntz代数的限制，通过一种新的方法阐明了描述费米子系统的CAR代数的结构。首先，嵌入，自同构，自同态，和各种表示的Cuntz代数明确构造。其次，将它们限制到Cuntz代数中的嵌入CAR代数，得到了CAR代数的相应结构。利用一类自同态，证明了作为费米子系统混合态的KMS态是由作为纯态的Fock表示得到的。这一结果与冯·诺依曼代数分类中的Araki-Woods因子理论相一致。通过限制自同构，明确地构造了费米子系统的各种非平凡时间演化，从而给出了可解费米子系统的新构造。对于规范理论中的不定度规费米子系统，伪Cuntz代数起着类似的作用。因此，问题 ...更多信息本文同样阐明了弦理论中FP鬼的表示，指出二维引力反常的存在不能用Alvarez-Gaume和维滕的推论来证明。它的缺点是混淆了T^*-乘积的数量和T-乘积的数量。与T积相反，T^* 积与时间微分互换，但某些场方程显然被打破。这个问题与异常无关。本文证明了Alvarez-Gaume和维滕的结果与场方程在T^*-乘积中的表观破裂在数量上是一致的.关于共形规范二维量子引力的可解性，我们研究了对应于无穷多个守恒量的无穷维对称性的构造.由于场方程作为共形规范条件的特殊性，很难定义作为对称生成元的一般守恒量的场的对称变换。这个过程对应于Noether定理的逆问题。少

项目成果

期刊论文数量（6）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Pseudo-Cuntz Algebra and Recursive Fermion System in String Theory

弦论中的伪Cuntz代数和递归费米子系统

DOI：
发表时间：
2003
期刊：
International Journal of Modern Physics A18
影响因子：
0
作者：
Nobuo Inagaki;Yutaka Kano;Nobuo Inagaki;Yutaka Kano;Etuo Kumagai;M.Abe
通讯作者：
M.Abe

Cuntz環からCAR環へ

从 Cuntz 环到 CAR 环

DOI：
发表时间：
2003
期刊：
数理解析研究所講究録 1333
影响因子：
0
作者：
Nobuo Inagaki;Yutaka Kano;Nobuo Inagaki;Yutaka Kano;Etuo Kumagai;M.Abe;Sigeo Aki;Shigeo Aki;M.Abe
通讯作者：
M.Abe

Nonlinear Transformation Group of CAR Fermion Algebra

CAR费米子代数的非线性变换群

DOI：
发表时间：
2002
期刊：
Letters in Mathematical Physics 60
影响因子：
0
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

From Cuntz Algebra to CAR Algebra

从 Cuntz 代数到 CAR 代数

DOI：
发表时间：
2003
期刊：
RIMS Kokyuroku 1333
影响因子：
0
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
通讯作者：
M.Abe