کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9518825 1346136 2005 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Smooth functional derivatives in Feynman path integrals by time slicing approximation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Smooth functional derivatives in Feynman path integrals by time slicing approximation
چکیده انگلیسی
We give a fairly general class of functionals on a path space so that Feynman path integral has a mathematically rigorous meaning. More precisely, for any functional belonging to our class, the time slicing approximation of Feynman path integral converges uniformly on compact subsets of the configuration space. Our class of functionals is closed under addition, multiplication, functional differentiation, translation and real linear transformation. The integration by parts and Taylor's expansion formula with respect to functional differentiation holds in Feynman path integral. Feynman path integral is invariant under translation and orthogonal transformation. The interchange of the order with Riemann-Stieltjes integrals, the interchange of the order with a limit, the semiclassical approximation and the fundamental theorem of calculus in Feynman path integral stay valid as well as N. Kumano-go [Bull. Sci. Math. 128 (3) (2004) 197-251].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Bulletin des Sciences Mathématiques - Volume 129, Issue 1, January 2005, Pages 57-79
نویسندگان
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