EXTRACTING LINEAR FACTORS IN FEYNMANS OPERATIONAL CALCULI : THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS

Title & Authors
EXTRACTING LINEAR FACTORS IN FEYNMANS OPERATIONAL CALCULI : THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS
Ahn, Byung-Moo;

Abstract
Disentangling is the essential operation of Feynmans 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 Feynmans operational calculus for time independent operators $\small{A_1, ... , A_n}$ and associated probability measures $\small{{\mu}_1,..., {\mu}_n}$. 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 Feynmans primary motivation for developing an operational calculus for noncommuting operators came from a desire to describe the evolution of certain quantum systems.m systems.
Keywords
Feynmans operational calculus;disentangling;
Language
English
Cited by
1.
METHODS FOR ITERATIVE DISENTANGLING IN FEYNMAN’S OPERATIONAL CALCULI : THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS,;

Journal of applied mathematics & informatics, 2010. vol.28. 3_4, pp.931-938
1.
Feynman’s Operational Calculi: Methods for Iterative Disentangling, Acta Applicandae Mathematicae, 2006, 92, 3, 293
2.
WEAK CONVERGENCE THEOREMS IN FEYNMAN'S OPERATIONAL CALCULI : THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS, Journal of the Chungcheong Mathematical Society , 2012, 25, 3, 531
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