Study of field theory and symmetries on continuum and latticized space-time

连续体和格子化时空的场论和对称性研究

• 批准号: 16540231
• 负责人: FUJIKAWA Kazuo
• 金额: $ 2.3万
• 依托单位: Nihon University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540231/
• 关键词: Gauge symmetry; path integral; magnetic monopole; second quantization; geometric phase; holonomy; quantum anomaly; gauge field; 隠れたゲージ対称性; 指数定理; 電荷の量子化; Q変形; 位相; トポロジー; 断熱近似; 非可換時空; ユニタリー性; 摂動; 真空状態

Fujikawa first examined the quantization of non-commutative space-time in the path integegral formulation, and showed that a modified time ordering prescription for space-time non-commutative theory, which preserves unitarity, inevitably breaks positive energy condition. He also studied the problem related to the small neutrino mass from a view point of the enhanced symmetry in the extended standard model when one sets the mass of the neutrino at zero.Fujikawa together with Deguchi presented a second quantized formulation of geometric phases, which allows the treatment of the geometric phases in path integral and operator formalism equally well. The hidden local symmetry appearing in this formulation has been further studied by Fujikawa, and it was shown that all the geometric phases are understood as holonomy associated with this hidden exact local symmetry in the Schroedinger equation. This new formulation is consistent with the basic superposition principle of quantum mechanics as well as the gauge invariance requirement of all the physical observables. The geometric phases thus arise from the hidden local symmetry appearing in second quantization.Deguchi studied the quantization of the magnetic monopole by using the Atiyah-Singer index theorem. Deguchi also studied the quantization of gauge filed on a sphere.Naka clarified the Q-deformation and non-local field theories in general.

藤川首先研究了路径积分公式中非交换时空的量子化，并表明时空非交换理论的修正时间排序规定在保持幺正性的情况下不可避免地会破坏正能量条件。他还从中微子质量为零时扩展标准模型中增强对称性的角度研究了与小中微子质量相关的问题。藤川与出口一起提出了第二个几何相位的量化公式，它允许路径积分和算子形式主义中几何相的处理同样好。藤川进一步研究了该公式中出现的隐藏局部对称性，结果表明所有几何相位都被理解为与薛定谔方程中隐藏的精确局部对称性相关的完整性。这个新的公式符合量子力学的基本叠加原理以及所有物理可观测量的规范不变性要求。因此，几何相位是由第二次量子化中出现的隐藏局部对称性产生的。出口利用Atiyah-Singer指数定理研究了磁单极子的量子化。出口还研究了球体上规范场的量子化。Naka总体上阐明了Q变形和非局域场论。

项目成果

Q-deformed bi-local fields. II

Q 变形双局域场。

• 发表时间: 2006
• 期刊: SIGMA 2
• 作者: H.Toyoda;S.Naka
• 通讯作者: S.Naka

Foundations of Quantum Mechanics in the Light of New Technology

新技术下的量子力学基础

• 发表时间: 2006
• 作者: Sachio Ishioka;Kazuo Fujikawa(編集)
• 通讯作者: Kazuo Fujikawa(編集)

Geometric phases, gauge symmetries and ray representation

几何相位、规范对称性和射线表示

• 发表时间: 2006
• 期刊: International Journal of Modern Physics A21
• 作者: Gundersen;G.G.;K.Tohge;K.Fujikawa
• 通讯作者: K.Fujikawa

Geometric pahses for mixed states and de-coherence

混合态和去相干的几何相

• 期刊: Annals of Physics (in press)
• 作者: R.Banerjee;S.Deguchi;Kazuo Fujikawa;K.Fujikawa;Kazuo Fujikawa;K.Fujikawa
• 通讯作者: K.Fujikawa

Geometric phases for mixed states and de-coherence

混合态和去相干的几何相位

• 期刊: Annals of Physics (in press)
• 作者: Kodama;T.;Tanaka;M.;Arimoto;N.;Yamada;T.et al.;K.Fujikawa
• 通讯作者: K.Fujikawa