1991 Fiscal Year Final Research Report Summary
The theory of unbounded derivations in C^* -algebras and its applications to statistical mechanics
| Project/Area Number |
01540157
|
|---|
| Research Category |
Grant-in-Aid for General Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
解析学
|
|---|
| Research Institution | Nihon University |
|---|
Principal Investigator |
SAKAI Shoichiro Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (30130503)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Masahiko Nihon University, College of Humanities and Sciences, Associate Professor, 文理学部, 助教授 (00171249)
SUZUKI Osamu Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (10096844)
MISONOU Yoshinao Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (20005705)
NIIRO Funio Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (50012191)
NIIRO Funio Nihon University, College of Humanities and Sciences, Professor (50012191)
|
|---|
| Project Period (FY) |
1989 – 1991
|
| Keywords | C^* -algebras / unbounded derivations / quantum statistical mechanics / continuous quantum systems / quantum lattice systems / operator algebras / phase transition / KMS states |
|---|
| Research Abstract |
This research is concerned with the theory of unbounded derivations in C^* -algebras, a subject whose study was motivated by quantum physics and statistical mechanics. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of the C^* -theory. The results concentrate on topics involving quantum statistical mechanics and differentiation in manifolds. One of the goals is to formulate the absence theorem of phase transitions in the most general form within the C^* -setting. For the first time, the principal investigator globally constructs within that setting, derivations for a fairly wide class of interaction models and present a new aidomatic treatment of the construction of time evolutions and KMS states.
|
