Feynman's Operational Calculi for Noncommuting Systems of Operators: Tensors, Ordered Supports, and Disentangling an Exponential Factor

In a recent paper, the authors presented the key ideas involved in their approach to Feynman's operational calculi for systems of not necessarily commuting bounded linear operators acting on a Banach space. The central objects of the theory are the disentangling algebra, a commutative Banach algebra, and the disentangling map which carries this commutative structure into the noncommutative algebra of operators. The study of properties of these disentangling maps will be pursued in this paper with an emphasis on (i) Feynman's formula for disentangling an exponential factor, and (ii) the effect on the disentangling map of ordered supports of some or all of the measures which govern the disentangling.