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Feynman's Operational Calculus and BeyondNoncommutativity and Time-Ordering$
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Gerald W Johnson, Michel L. Lapidus, and Lance Nielsen

Print publication date: 2015

Print ISBN-13: 9780198702498

Published to Oxford Scholarship Online: September 2015

DOI: 10.1093/acprof:oso/9780198702498.001.0001

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Disentangling via Tensor Products and Ordered Supports

Disentangling via Tensor Products and Ordered Supports

(p.63) 3 Disentangling via Tensor Products and Ordered Supports
Feynman's Operational Calculus and Beyond

Gerald W. Johnson

Michel L. Lapidus

Lance Nielsen

Oxford University Press

More involved types of disentanglings are considered in this chapter. We discuss the situation where the Banach space X can be written as a direct sum X=Y⊕Z, for some Banach spaces Y and Z, and each of the operators Ai can be decomposed as Ai=Bi⊕Ci, for i=1,…,n. A second type of disentangling discussed is that of a function which is symmetric in several of its variables. Next, consideration is given to the disentangling of certain analytic (i.e. holomorphic) functions which can be written as tensor products of analytic functions of one variable. Also discussed is the effect on the disentangling process of the use of time-ordering measures with ordered supports. The results obtained in this part of Chapter 3 play a role throughout the remainder of the book. Finally, the disentangling of so-called exponential factors is addressed; we track the occurrence of a particular operator in the time-ordered products that constitute the disentangling.

Keywords:   disentangling, ordered support, tensor product, exponential factor

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