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Set Theory, Topology and Banach Spaces (Second International Topology Conference in Kielce)
July 7-11, 2008
Institute of Mathematics, Jan Kochanowski University in Kielce; co-organized by Technical University of Lodz
Kielce, Poland

Organizers
Taras Banakh, Piotr Koszmider, Wieslaw Kubis

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Measure permutation formulas in Feynman's operational calculi
by
Byoung Soo Kim
School of Liberal Arts, Seoul National University of Technology, Seoul 139-743, Korea

It is important in several areas of mathematics and its applications to be able to form functions of operators. In 1951 R. Feynman invented some rules, in his paper "An operator calculus having applications in quantum electrodynamics", for forming functions of noncommuting operators. The most extensively studied and applied approach to Feynman's operational (or functional) calculus is the noncommutative operational calculus created by V. Maslov in the early 1970's. Recently Jefferies and Johnson developed a mathematically rigorous approach to Feynman's operational calculi. We introduce some basic properties of these two approaches. Also we discuss the measure permutation formulas in Jefferies-Johnson's theory of Feynman's operational calculi. These formulas correspond to the index permutation formula in Maslov's discretised version of Feynman's operational calculus.

Date received: June 7, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxg-07.