Path integrals - Expansion of analysis on path space by time slicing approximation
| Project/Area Number |
24540193
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Kogakuin University |
|---|
Principal Investigator |
KUMANOGO NAOTO 工学院大学, 基礎・教養教育部門, 教授 (40296778)
|
|---|
| Project Period (FY) |
2012-04-01 – 2015-03-31
|
| Project Status |
Completed (Fiscal Year 2014)
|
| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Keywords | 経路積分 / 関数方程式論 / 関数解析学 / 数理物理 / 擬微分作用素 / フーリエ積分作用素 / 振動積分 / 確率解析 / 関数方程式 / 確率論 |
|---|
| Outline of Final Research Achievements |
We gave a general class of functionals for which the phase space path integrals of higher order parabolic type have a mathematically rigorous meaning. For any functional belonging to this class, the time slicing approximation of the phase space path integral, converges uniformly on compact subsets with respect to the endpoint of position paths and to the starting point of momentum paths. Because this class of functionals is closed under addition and multiplication, we can produce many functionals which are path integrable. Furthermore, though we need to pay attention for use, the interchange of the order of the phase space path integrals and some integrals, and the interchange of the order of the phase space path integrals and some limit operations, are valid.
|
Report
(4 results)
Research Products
(12 results)
