|
Organizers |
Iterative disentangling in Feynman’s operational calculi
by
Byoung Soo Kim
Seoul National University of Technology, Seoul, Korea
Coauthors: Kun Soo Chang
It is important in several areas of mathematics and its applications to be able to form functions of operators. If one has a single self-adjoint or several commuting self-adjoint operators, the spectral theorem provides an extremely rich functional calculus. However, as soon as we have two or more noncommuting operators, the functional calculus becomes much more complicated. Feynman invented some ’rules’ for forming functions of noncommuting operators. We introduce an approach to Feynman’s operational calculus for systems of bounded, not necessarily commuting, linear operators acting on a Banach space. In particular, formulas which simplify ’disentangling’ under various conditions are given. The operation of disentangling is the key to Feynman’s operational calculi.
Date received: June 9, 2005
Copyright © 2005 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 # carf-13.