An Integral Equation for Feynman's Operational Calcului

TL;DR

This paper derives an integral equation for Feynman's operational calculus, linking it to evolution equations and demonstrating its application to heat and Schrödinger equations, while connecting it to analytic Feynman integrals.

Contribution

It introduces a new integral equation for Feynman's operational calculus and relates it to existing evolution equations and analytic Feynman integrals.

Findings

Derived an integral equation for Feynman's operational calculus.

Showed how solutions to heat and Schrödinger equations can be obtained.

Connected operational calculus with analytic Feynman integrals.

Abstract

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.