Extracting linear factors in Feynman's oerational calculi : The case of time dependent noncommuting operators
Bull. Korean Math. Soc. 2004 Vol. 41, No. 3, 573-587
Published online September 1, 2004
Byung Moo Ahn
Soonchunhyang University Asan
Abstract : Disentangling is the essential operation of Feynman's operational calculus for noncommuting operators. Thus formulas which simplify this operation are central to the subject. In a recent paper the procedure for ``extracting a linear factor'' has been established in the setting of Feynman's operational calculus for time independent operators $ A_1 , \cdots , A_n $ and associated probability measures $\mu_1 , \cdots , \mu_n $. While the setting just described is natural in many circumstances, it is not natural for evolution problems. There the measures should not be restricted to probability measures and it is worthwhile to allow the operators to depend on time. The main purpose for this paper is to extend the procedure for extracting a linear factor to this latter setting. We should mention that Feynman's primary motivation for developing an operational calculus for noncommuting operators came from a desire to describe the evolution of certain quantum systems.
Keywords : Feynman's operational calculus, disentangling
MSC numbers : 47A60
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