Project/Area Number  04804014 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
核・宇宙線・素粒子

Research Institution  Toyama University 
Principal Investigator 
HIRAYAMA Minoru Toyama University, Department of Physics, Professor, 理学部, 教授 (80018986)

CoInvestigator(Kenkyūbuntansha) 
田島 俊彦 富山工業高等専門学校, 教授 (20027353)
HOSONO Shinobu Toyama University, Department of Mathematics, Associate Professor, 理学部, 助教授 (60212198)
HAMAMOTO Shinji Toyama University, Department of Physics, Associate Professor, 理学部, 助教授 (80018994)
MATUMOTO Keniti Toyama University, Department of Physics, Professor, 理学部, 教授 (90019456)
YAMAKOSHI Hitoshi Toyama National College of Technology, Lecturer, 講師 (70249770)

Project Fiscal Year 
1992 – 1994

Project Status 
Completed(Fiscal Year 1994)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1994 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1993 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1992 : ¥600,000 (Direct Cost : ¥600,000)

Keywords  Quantum group / Gauge field / 量子郡 / ゲージ場 / 量子群 / quantum group / gauge field 
Research Abstract 
Although we have tried to formulate the quantum field theory which possesses a quantumgroup gauge symmetry, we have not succeeded in it until now. On the other hand, since the discovery of the geometric phase by Berry, it has been clarified that some quantum mechanical and quantum field theoretic models possess gaugetheoretic structures. Berry found it in the case of quantum mechanics with adiabatically changing environment. The similar structure exists, however, in more general systems where a fast mode of motion and a slow one coexist. In the case of Berry's phase factor, the gauge potential A is given by a parameterdependent state vector and its timederivative. The field strength F constructed from A can also be described as the imaginary part of a gaugeinvariant complex quantity T.The real part G of T has not been investigated so intensively. It can be interpreted, however, as the metric of the space of parameterdependent state vectors (projective Hilbert space). By making use of this fact, Anandan and Aharonov succeeded in deriving a new type of uncertainly relation. By the research in this year, we generalized the abovementioned relation. The Grassmann manifold is a natural generalization of the projective Hilbert space and can be regarded as the space of sets of some orthonormal state vectors. Obtaining the distance formula for the Grassmann manifold, we succeeded in deriving the timeenergy uncertainty relation satisfied by a set of orthonormal vectors.
