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Exponentials of noncommuting operators via Feynman's operational calculus, and associated evolution equations
Abstract
In a 1951 paper, R. P. Feynman presented a heuristic method for forming functons of noncommuting operators. B. DeFacio, G. W. Johnson and M.L. Lapidus tackled the task of putting mathematical rigor to Feynman's ideas. Following their lead, this paper uses the heuristic ideas put forth by Feynman to obtain perturbation series for exponentials of sums of noncommuting operators. The disentangling is provided by the measures on the time intervals under consideration. We consider continuous measures as well as measures with a finite number of nonzero discrete parts. We then show that the perturbation series so obtained is the solution to an integral equation, that is, an evolution equation in integral form.
Subject Area
Mathematics
Recommended Citation
Reyes, Jose Tristan Fua, "Exponentials of noncommuting operators via Feynman's operational calculus, and associated evolution equations" (1995). ETD collection for University of Nebraska-Lincoln. AAI9615000.
https://digitalcommons.unl.edu/dissertations/AAI9615000