2011 Fiscal Year Final Research Report
Path integrals as analysis on path space by time slicing approximation
| Project/Area Number |
21540196
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kogakuin University |
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Principal Investigator |
KUMANOGO Naoto 工学院大学, 基礎・教養教育部門, 教授 (40296778)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 経路積分 / 関数方程式 / 関数解析学 / 数理物理 / 振動積分 / 擬微分作用素 / 準古典近似 / 確率解析 |
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| Research Abstract |
Using the time slicing approximation via piecewise constant paths, we gave two general classes of functionals for which the phase space Feynman path integrals have a mathematically rigorous meaning. Each class is closed under addition, multiplication, translation, linear transformation and functional differentiation. Furthermore, though we need to pay attention for use, we proved the interchange of the order with some integrals and some limits, natural properties under translation and orthogonal transformation, the integration by parts with respect to functional differentiation, and the semiclassical approximation of Hamiltonian type in the phase space path integrals.
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