Study of the Feynman - Dyson Calculus (MRI Planning Grant)

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This is a Minority Research Initiative Planning Grant proposal. Professor Gill works in the area of operator theory on Banach spaces with applications to mathematical physics. In recent years, Professor Gill has been working on an analytic approach to the Feynman Dyson calculus, a conceptual operator theoretic approach to problems that arose in quantum electrodynamics. The efforts of Professor Gill apply to linear evolutions on reflexive Banach spaces, and he proposes to remove the reflexivity restriction, allow for minimal domain considerations, and to extend the theory to nonlinear evolutions. He plans to consult with experts on these scientific matters, thereby enhancing his research program and elevating its level of effectiveness for further funding support.