Generalized Quantization, its Representations and Relations to Field Theory

广义量化、其表示以及与场论的关系

• 批准号: 10640394
• 负责人: OHNUKI Yshio
• 金额: $ 1.41万
• 依托单位: Nagoya Women's University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640394/
• 关键词: constrained system; canonical quantization; induced representation; gauge structure; Dirac's quantization; D-dimensional sphere; chiral manifold; Grassmann manifold; ゲージポテンシャル

Although quantization is one of the fundamental concepts in physics, its deep meaning is not yet very clear. Especially, it is known that the canonical quantization usually adopted is not applicable to a system constrained on a finite manifold. For this reason, about 50 years ago, modifying the canonical formalism Dirac proposed a new method of quantization for a constrained system. However it explicitly depend on the dynamics under consideration. On the other hand several years ago we argued another approach to this problem from somewhat different point of view. Applying it to a system constrained to move on SィイD1DィエD1 we have found emergence of a remarkable type of gauge potentials in quantizing the system. We have also shown that they can be obtained as a connection on the cosset space SO(D+1)/SO(D)〜SィイD1DィエD1, Using this technique we have examined the gauge structures in quantizing the respective systems on the chiral manifold SUィイD2LィエD2(n)×UィイD2RィエD2(n)/UィイD2VィエD2(n) and the Gras … More smann manifold SU(m+n)/SU(n)×SU(m). As a result it has been shown that gauge potentials in the former case become position-independent under suitable choice of the gauge while in the latter case they are given in integral forms. A review talk about our study on these problems was delivered at the International Workshop held in Varna in 1998, and published, in 1999, in the Proceedings of the Workshop. Through these investigations some limits of applicability of our quantization have also become clear. Extension of our quantization to a system on a manifold without geometric symmetry has been concluded to be impossible. Ii comes frome non-integrable structure of displacements connecting of two point on the manifold. In spite of this when combining our quantization technique to Dirac formalism we can detemine all possible irreducible representations of the Dirac algebra for a system constrained on a deformed manifold diffeomorphic to SィイD1DィエD1 under the Hamiltonian with potential interaction. The result has been reported in the International Conference held at Kiev in 1999. Furthermore generalization of our quantization scheme to filed theory has been found to be impossible without deserting the global structure of the manifold on which the field is constrained. A detail of this argument was delivered at the 6th Winger Symposium held at Istanbul in 1999. Less

虽然量子化是物理学中的基本概念之一，但它的深层含义还不是很清楚。特别地，已知通常采用的正则量子化不适用于有限流形上的系统。为此，大约50年前，修改正则形式主义的狄拉克提出了一种约束系统的新量子化方法。然而，它显然取决于所考虑的动态。另一方面，几年前，我们从不同的角度提出了另一种解决这个问题的方法。将它应用于一个在S_（？）D_（？）D_（？）D_（？）D_1上运动的系统，我们发现在量子化系统时出现了一种引人注目的规范势。我们还证明了它们可以作为cosset空间SO（D+1）/SO（D）<$S <$D 1 D <$D 1上的一个联系得到。利用这种方法，我们研究了手征流形SU_n D 2 L_n D 2（n）×U_n D 2 R_n D 2（n）/U_n D 2 V_n D 2（n）上量子化相应系统时的规范结构，并研究了Gas ...更多信息 smann流形SU（m+n）/SU（n）×SU（m）.结果表明，在前一种情况下，规范势在适当选择规范的情况下变得与位置无关，而在后一种情况下，它们以积分形式给出。1998年在瓦尔纳举行的国际讲习班上发表了关于我们对这些问题的研究的评论性讲话，并于1999年发表在讲习班会议记录上。通过这些研究，我们的量子化的适用性的一些限制也变得清晰。将我们的量子化推广到没有几何对称性的流形上的系统是不可能的。Ii来自流形上两点位移连接的不可积结构。尽管如此，当我们把量子化技术与狄拉克形式结合起来时，我们可以确定一个约束在变形流形上的系统的狄拉克代数在具有势相互作用的哈密顿量下的所有可能的不可约表示。1999年在基辅举行的国际会议上报告了这一成果。此外，推广我们的量子化方案领域的理论已被发现是不可能的，而不放弃的全球结构的流形上的领域的约束。1999年在伊斯坦布尔举行的第六届温格研讨会上详细阐述了这一论点。少

项目成果

大貫義郎: "『物理学の20世紀』朝日選書619,第9章 対称性の発見-坂田模型からクオークへ-"朝日新聞社. 20 (1999)

大贯义郎：《20世纪物理学》《朝日新闻》619，第9章对称性的发现 - 从坂田模型到夸克 - 朝日新闻 20 (1999)。

Yoshio OHNUKI: "Quantization on Closed Manifold"Proc. of IV Int. Workshop on Complex Structures and Vector Fields (eds. S. Dimiev et al, World Scientific). 266-288 (1999)

Yoshio OHNUKI：“闭流形上的量化”Proc。

Y.Ohnuki: "Quantization on Closed Manifolds" Proc.of Fourth International Workshop on Complex Structures and Vector Fields. 印刷中.

Y. Ohnuki：第四届复杂结构和矢量场国际研讨会的“封闭流形的量化”论文集。

Yoshio OHNUKI: "Quantization on Manifolds Diffeomorphic to S^D and Induced Gauge Potentials"Proc. of the 5th Int. Wigner Symposium (eds. P.Kasperkovitz et al, International Press). 509-512 (1999)

Yoshio OHNUKI：“S^D 微分流形的量化和感应规范势”Proc。

Yoshio OHNUKI: "Quantization on Closed Manifolds"Proc. of IV Int. Workshop on Complex Structures and Vector Fields (eds. S.Dimiev et al, World Scientific). 266-288 (1999)

Yoshio OHNUKI：“闭流形的量化”Proc。