The map from the commutative algebra to the noncommutative algebra of operators is the essential operation of Feyn- man's operational calculus for noncommuting operators. Thus formulas which simplify this operation are meaningful to the subject. In a recent paper the procedure for for iterative disentangling has been es- tablished in the setting of Feynman's operationalcalculus for time indepen- dent operatorsA1, · · · ,An and associatedprobabilitymeasures µ1, · · · ,µn. The main purpose for this paper is to extend the procedure for methods for iterative to time dependent operators.
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
A1,...,An and associated probability measures
μ1,...,μn . 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.m systems.