The second term of the semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth

この論文にアクセスする

この論文をさがす

著者

抄録

Recently N. Kumano-go [<b>15</b>] succeeded in proving that piecewise linear time slicing approximation to Feynman path integral<br>\int F(\gamma)e^{i\nu S(\gamma)}\,\mathscr{D}[\gamma]<br>actually converges to the limit as the mesh of division of time goes to 0 if the functional <i>F</i>(γ) of paths γ belongs to a certain class of functionals, which includes, as a typical example, Stieltjes integral of the following form;<br>\begin{equation}\label{stieltjesint}%1F(\gamma) = \int_0^T f(t,\gamma(t)) \rho(dt), \tag{1}\end{equation}<br>where ρ(<i>t</i>) is a function of bounded variation and <i>f</i>(<i>t</i>, <i>x</i>) is a sufficiently smooth function with polynomial growth as |<i>x</i>| → ∞. Moreover, he rigorously showed that the limit, which we call the Feynman path integral, has rich properties (see also [<b>10</b>]).<br>The present paper has two aims. The first aim is to show that a large part of discussion in [<b>15</b>] becomes much simpler and clearer if one uses piecewise classical paths in place of piecewise linear paths.<br>The second aim is to explain that the use of piecewise classical paths naturally leads us to an analytic formula for the second term of the semi-classical asymptotic expansion of the Feynman path integrals under a little stronger assumptions than that in [<b>15</b>]. If <i>F</i>(γ) ≡ 1, this second term coincides with the one given by G. D. Birkhoff [<b>1</b>].

収録刊行物

  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 58(3), 837-867, 2006-07-01 

    The Mathematical Society of Japan

参考文献:  17件

参考文献を見るにはログインが必要です。ユーザIDをお持ちでない方は新規登録してください。

各種コード

  • NII論文ID(NAID)
    10018381149
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    7987167
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  J-STAGE 
ページトップへ