Path integrals as analysis on path space by time slicing approximation

通过时间切片近似对路径空间进行路径积分分析

• 批准号: 21540196
• 负责人: KUMANOGO Naoto
• 金额: $ 2.91万
• 依托单位: Kogakuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540196/
• 关键词: 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; フーリエ積分作用素; 確率論

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.

使用分段常数路径切片近似的时间，我们给出了两个一般类别的功能类别，相位空间Feynman路径积分具有数学上严格的含义。每个类都在加法，乘法，翻译，线性转换和功能分化下关闭。此外，尽管我们需要注意使用，但我们证明了该顺序与某些积分和某些限制，翻译和正交转换的自然特性的互换，各部分相对于功能差异化的集成以及汉密尔顿类型在相位空间路径积分中的半经典近似。

项目成果

Feynman integrals

费曼积分

• 发表时间: 2009
• 作者: Naoto Kumano-go;Daisuke Fujiwara;Naoto Kumano-go;古谷康雄;熊ノ郷直人;古谷康雄;Naoto Kumano-go;熊ノ郷直人;Tokio Matsuyama;Tokio Matsuyama;熊ノ郷直人;T.Matsuyama;Naoto Kumano-go;Naoto Kumano-go;熊ノ郷直人;Naoto Kumano-go;熊ノ郷直人;Naoto Kumano-go;Naoto Kumano-go;熊ノ郷直人;Naoto Kumano-go;Naoto Kumano-go;Naoto Kumano-go
• 通讯作者: Naoto Kumano-go

Phase space Feynman path integrals via piecewise bicharacteristic paths and their semiclassical approximations

• DOI: 10.1016/j.bulsci.2007.06.003
• 发表时间: 2008-06-01
• 期刊: BULLETIN DES SCIENCES MATHEMATIQUES
• 影响因子: 1.3
• 作者: Kumano-go, Naoto;Fujiwara, Daisuke
• 通讯作者: Fujiwara, Daisuke

Phase space Feynman path integrals and their semi-classical approximations

相空间费曼路径积分及其半经典近似

• 发表时间: 2009
• 作者: Naoto Kumano-go;Daisuke Fujiwara;Naoto Kumano-go;古谷康雄;熊ノ郷直人;古谷康雄;Naoto Kumano-go;熊ノ郷直人;Tokio Matsuyama;Tokio Matsuyama;熊ノ郷直人;T.Matsuyama;Naoto Kumano-go;Naoto Kumano-go;熊ノ郷直人;Naoto Kumano-go;熊ノ郷直人;Naoto Kumano-go;Naoto Kumano-go;熊ノ郷直人;Naoto Kumano-go
• 通讯作者: Naoto Kumano-go

Phase space Feynman path integrals via piecewise bicharacteristic paths and their semiclasscial approximations

通过分段双特征路径的相空间费曼路径积分及其半经典近似

• 发表时间: 2010
• 作者: Naoto Kumano-go;Daisuke Fujiwara;Naoto Kumano-go;古谷康雄;熊ノ郷直人;古谷康雄;Naoto Kumano-go;熊ノ郷直人;Tokio Matsuyama;Tokio Matsuyama;熊ノ郷直人;T.Matsuyama;Naoto Kumano-go;Naoto Kumano-go;熊ノ郷直人;Naoto Kumano-go;熊ノ郷直人;Naoto Kumano-go
• 通讯作者: Naoto Kumano-go

Phase space Feynman path integrals by time slicing approximation

通过时间切片近似的相空间费曼路径积分

• 发表时间: 2011
• 作者: Naoto Kumano-go;Daisuke Fujiwara;Naoto Kumano-go;古谷康雄;熊ノ郷直人;古谷康雄;Naoto Kumano-go;熊ノ郷直人;Tokio Matsuyama;Tokio Matsuyama;熊ノ郷直人;T.Matsuyama;Naoto Kumano-go
• 通讯作者: Naoto Kumano-go