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Combinatorial and commutative manipulations in Feynman's Operational Calculi for noncommuting operators

Duane Einfeld, University of Nebraska - Lincoln

Abstract

In Feynman's Operational Calculi, a function of indeterminates in a commutative space is mapped to an operator expression in a space of (generally) noncommuting operators; the image of the map is determined by a choice of measures associated with the operators, by which the operators are 'disentangled'. Results in this area of research include formulas for disentangling in particular cases of operators and measures. We consider two ways in which this process might be facilitated. First, we develop a set of notations and operations for handling the combinatorial arguments that tend to arise. Second, we develop an intermediate space for the disentangling map, where commutativity might be exploited more extensively.^

Subject Area

Mathematics

Recommended Citation

Einfeld, Duane, "Combinatorial and commutative manipulations in Feynman's Operational Calculi for noncommuting operators" (2009). ETD collection for University of Nebraska - Lincoln. AAI3350445.
http://digitalcommons.unl.edu/dissertations/AAI3350445

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