Chapter

Disentangling via Tensor Products and Ordered Supports

Gerald W. Johnson, Michel L. Lapidus and Lance Nielsen

in Feynman's Operational Calculus and Beyond

Published in print August 2015 | ISBN: 9780198702498
Published online September 2015 | e-ISBN: 9780191772160 | DOI: https://dx.doi.org/10.1093/acprof:oso/9780198702498.003.0003
Disentangling via Tensor Products and Ordered Supports

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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

Chapter.  20732 words. 

Subjects: Mathematical and Statistical Physics ; Mathematics

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