Grant-in-Aid for Scientific Research (B).
|Research Institution||Science University of Tokyo|
OMORI Hideki Science University of Tokyo, Dept.Math. Science and Technology, Prof., 理工学部, 教授 (20087018)
YOOHIOKA Akira Science University of Tokyo, Science and Technology, Dept.Math.Asso.Prof., 理工学部, 助教授 (40200935)
大槻 舒一 東京理科大学, 理工学部, 教授 (80112895)
SHOJI Toshiaki Science University of Tokyo, Science and Technology, Dept.Math.Prof., 理工学部, 教授 (40120191)
小林 嶺道 東京理科大学, 理工学部, 教授 (70120186)
ARAKI Fujihiro Science University of Tokyo, Science and Technology, Dept.Math.Prof., 理工学部, 教授 (20027361)
原 民夫 東京理科大学, 理工学部, 講師 (10120205)
田宮 高紀 東京理科大学, 理工学部, 講師 (60183472)
OKA Hasatoshi Science University of Tokyo, Science and Technology, Dept.Math.Prof., 理工学部, 教授 (70120178)
FURUTANI Kense Science University of Tokyo, Science and Technology, Dept.Math.Prof., 理工学部, 教授 (70112901)
|Project Fiscal Year
1997 – 2000
Completed(Fiscal Year 2000)
|Budget Amount *help
¥7,200,000 (Direct Cost : ¥7,200,000)
Fiscal Year 2000 : ¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1999 : ¥1,900,000 (Direct Cost : ¥1,900,000)
Fiscal Year 1998 : ¥1,600,000 (Direct Cost : ¥1,600,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)
|Keywords||non commutative geometry / star-product (*-product) / non commutative differential geometry / 非可換幾何学 / *一積 / 非可換微分幾何学 / *-積 / 水一積 / 幾何学的量子化|
The field of deformation quatization is one of the most active, intersecting area of mathematics and physics.
There are several kernel places in the world, working to making quantum calculus. It was very important and fruitful to discuss with many people who are interested in this field.
In this period of research, the following are discovered :
The notion of μ regulated algebras can be the most fundamental notion for the quantum calculus, and for the non-commutative differential geometry, even for the case the Plank constant h is viewed as a genuine parameter moving in positive reals.
In such system, we found special elements, that play the same role as vacuum in the classical quantum theory.
In the case that h is viewed as a positive real parameter, it is crucial to fix the product formula, for the star-exponential functions of quadratic forms.
Here we found strange phenomena that quadratic forms with non-vanishing discriminant have two different inverses and therefore the associativity breaks down.
By this phenomenon, we are forced to break some symmetry in order to keep associativity. Infact, we have to use SL (2 ; R)-symmetry instead of SL(2 ; C)-symmetry.