Feynman's operational calculi: Disentangling away from the origin

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Abstract

In this paper we develop a method of forming functions of noncommuting operators (or disentangling) using functions that are not necessarily analytic at the origin in ℂ n . The method of disentangling follows Feynman's heuristic rules from in (Feynman in Phys. Rev. 84:18-128, 1951) a mathematically rigorous fashion, generalizing the work of Jefferies and Johnson and the present author in (Jefferies and Johnson in Russ. J. Math. 8:153-181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193-226, 2001). In fact, the work in (Jefferies and Johnson in Russ. J. Math. 8:153-181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193-226, 2001) allow only functions analytic in a polydisk centered at the origin in ℂ n while the method introduced in this paper enable functions that are not analytic at the origin to be used. It is shown that the disentangling formalism introduced here reduces to that of (Jefferies and Johnson in Russ. J. Math. 8:153-181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193-226, 2001) under the appropriate assumptions. A basic commutativity theorem is also established.

Original languageEnglish (US)
Pages (from-to)409-429
Number of pages21
JournalActa Applicandae Mathematicae
Volume110
Issue number1
DOIs
StatePublished - Apr 1 2010

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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