کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4582446 1333806 2011 39 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Feynman operator calculus: The constructive theory
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Feynman operator calculus: The constructive theory
چکیده انگلیسی

In this paper, we survey progress on the Feynman operator calculus and path integral. We first develop an operator version of the Henstock–Kurzweil integral, construct the operator calculus and extend the Hille–Yosida theory. This shows that our approach is a natural extension of operator theory to the time-ordered setting. As an application, we unify the theory of time-dependent parabolic and hyperbolic evolution equations. Our theory is then reformulated as a sum over paths, providing a completely rigorous foundation for the Feynman path integral. Using our disentanglement approach, we extend the Trotter–Kato theory.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Expositiones Mathematicae - Volume 29, Issue 2, 2011, Pages 165–203
نویسندگان
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