Quantum theory of gauge fields, and fermions and solitons

藤川调查领域理论的晶格，特别是可能性的新狄拉克运营商的费米子。他还研究了定义马约拉纳费米子的晶格和CP对称性等，并研究了定义超对称的晶格。在路径积分框架下分析了时空非对易理论的么正性问题。给出了路径积分中自旋统计定理的一个新表述，研究了具有孤子解的二维超对称理论的一种反常，Fujikawa还研究了Schroedinger问题中几何相位中规范对称性的起源，阐明了手征反常与几何相位的根本区别. Tsutsui研究了具有奇异势的量子理论的数学性质，发现了一些有趣的现象，如超对称性、对偶性和Berry相位。他还扩大了制定，包括潜在的含有分歧和审查的影响奇异性的光谱。特别是，它表明，一个hind的复制状态是可能的，当潜在的诱导焦散线。通过研究量子阱压力的温度依赖性，他表明它对阱中粒子的统计敏感。量子奇异性可以作为量子比特用于量子计算。Tsutui还将博弈论作为纠缠的一个应用进行了量子化，并详细研究了纠缠对博弈论稳定解的影响。通过使用被称为施密特分解的混合态表示法，他成功地构建了一个比以前已知的更一般的理论框架。

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.