An Integral Equation for Feynman's Operational Calcului

Details An Integral Equation for Feynman's Operational Calcului An Integral Equation for Feynman's Operational Calcului

2009-12-16

arxiv.org/abs/0912.3041v1

Integration: Mathematical Theory and Applications, 1 (2008), 49-66

Mathematics

Functional Analysis

17 pages

Scientific paper

In this paper we develop an integral equation satisfied by Feynman's operational calculi in formalism of B. Jefferies and G. W. Johnson. In particular a "reduced" disentangling is derived and an evolution equation of DeFacio, Johnson, and Lapidus is used to obtain the integral equation. After the integral equation is presented, we show that solutions to the heat and Schrodinger's equation can be obtained from the reduced disentangling and its integral equation. We also make connections between the Jefferies and Johnson development of the operational calculi and the analytic Feynman integral.

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