| Project/Area Number |
13135206
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
|
| Allocation Type | Single-year Grants |
|---|
| Review Section |
Science and Engineering
|
|---|
| Research Institution | Nihon University (2004-2006)
The University of Tokyo (2001-2003) |
|---|
Principal Investigator |
FUJIKAWA Kazuo Nihon University, Coll. Of Sc. And Tech., Professor (30013436)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TSUTSUI Izumi Nihon University, High Energy Acc. Lab., Theory Div., Assoc. Professor (10262106)
|
|---|
| Project Period (FY) |
2001 – 2006
|
| Project Status |
Completed (Fiscal Year 2006)
|
| Budget Amount *help |
¥10,300,000 (Direct Cost: ¥10,300,000)
Fiscal Year 2006: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2005: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2004: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2003: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2002: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2001: ¥1,700,000 (Direct Cost: ¥1,700,000)
|
|---|
| Keywords | Choral anomaly / Lattice gauge theory / Gauge symmetry / Geometric phase / Quantum theory with singular potential / Statistics / Quantum game theory / Entanglement / 隠れたゲージ対称性 / ホロノミー / 量子エンタングルメント / ゲーム理論 / 位相 / 断熱近似 / ハミルトニアン / 可解系 / 経路積分 / 自然さ / ソリトン / 量子縺れ / カイラル対称性 / Dirac演算子 / 局所性 / 超対称性 / 量子圧 / 非可換空間 / 双対性 / Berry位相 / 量子コピー / フェルミ演算子 / 素粒子論 / 数理物理 / トポロジー / ゲージ理論 |
|---|
| Research Abstract |
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.
|
