Feynman's Operational Calculi: Methods for Iterative Disentangling

Authors: Jefferies, B.¹; Johnson, G.²; Kim, B.³

Source: Acta Applicandae Mathematicae, Volume 92, Number 3, July 2006 , pp. 293-309(17)

Publisher: Springer

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Abstract:

The disentangling map from the commutative disentangling algebra to the noncommutative algebra of operators is the central feature of Feynman's time-ordered operational calculi for noncommuting operators. Therefore, formulas which simplify the disentangling process are important to the subject. The results of this paper permit us under appropriate assumptions to reduce the disentangling process to an iterated sequence of simpler disentanglings. Earlier results can be combined with the main results here to yield further corollaries and examples some of which will be given in this paper.

Keywords: Feynman's operational calculi for noncommuting operators; disentangling; iterated disentangling; disentangling a multilinear factor; Primary 47A60; Secondary 46J15, 81Q30, 81S99

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10440-006-9061-2

Affiliations: 1: Email: b.jefferies@unsw.edu.au 2: Email: gjohnson@math.unl.edu 3: Email: mathkbs@snut.ac.kr

Publication date: 2006-07-01