Quantum theory of gauge fields, and fermions and solitons

规范场、费米子和孤子的量子理论

基本信息

批准号：
13135206
负责人：
FUJIKAWA Kazuo
金额：
$ 6.59万
依托单位：
Nihon University (2004-2006)The University of Tokyo (2001-2003)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2006
项目状态：
已结题

项目摘要

Fujikawa investigated field theory on the lattice, in particular, the possibility of new Dirac operators for fermions. He also studied the definition of Majorana fermions on the lattice and CP symmetry among others and studied the definition of supersymmetry on the lattice. The unitarity issue of space-time non-commutative theory was analyzed in path integral framework. Gave a new formulation of spin-statistics theorem in path integral, and investigated a kind of anomaly for a 2-dimensional supersymmetric theory with soliton solutions.Fujikawa also studied the origin of gauge symmetry in the geometric phases in Schroedinger problem, and clarified the basic difference detween the chiral anomaly and the geometric phase. It was shown that all the geometric phases are understood as holonomy associated with the exact hidden local symmetry in Schroedinger equation.Tsutsui investigated the mathematical property of quantum theory with singular potentials, and found interesting phenomena such as supersymmetry, duality and Berry's phase. He also extended the formulation to include the potential which contains divergence and examined the effects of the singularity on spectra. In particular, it was shown that a hind of copying states is possible when the potential induces caustics. By investigating the temperature dependence of the pressure for a quantum well, he showed that it is sensitive to statistics of particles in the well. It was alson shown that the quantum singularity is used as a qubit in quantum computation. A solution more general than previously known was obtained for the case of N=3 in the soluble Calogero model with singular potential.Tsutui also quantized the game theory as an application of entanglement and studied in detail the effects of entanglement on the stable solutions in game theory. By using the representation of mixed states called Schmidt decomposition, he succeeded in constructing a more general theoretical framework than previously known ones.

藤川研究了晶格场论，特别是费米子的新狄拉克算子的可能性。他还研究了晶格上马约拉纳费米子的定义和CP对称性等，并研究了晶格上超对称性的定义。在路径积分框架下分析了时空非交换理论的幺正性问题。给出了路径积分中自旋统计定理的新表述，并研究了具有孤子解的二维超对称理论的一种反常现象。藤川还研究了薛定谔问题中几何相位规范对称性的起源，阐明了基本原理手性反常和几何相位之间的差异。结果表明，所有的几何相位都可以理解为与薛定谔方程中精确的隐局域对称性相关的完整性。筒井研究了奇异势量子论的数学性质，发现了诸如超对称性、对偶性和贝里相位等有趣的现象。他还扩展了该公式以包括包含散度的势，并检查了奇点对光谱的影响。特别是，研究表明，当电势引起焦散时，复制状态的后继是可能的。通过研究量子阱压力与温度的关系，他表明它对量子阱中粒子的统计数据很敏感。研究还表明，量子奇点在量子计算中被用作量子位。对于具有奇异势的可溶Calogero模型中N=3的情况，得到了比以前已知的更通用的解。Tsutui还将博弈论量化为纠缠的应用，并详细研究了纠缠对博弈中稳定解的影响理论。通过使用称为施密特分解的混合态表示，他成功地构建了一个比以前已知的更通用的理论框架。