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

这是一份少数民族研究计划拨款提案。吉尔教授的研究领域是巴拿赫空间的算子理论及其在数学物理中的应用。近年来，吉尔教授一直致力于费曼戴森微积分的解析方法，这是一种解决量子电动力学中出现的问题的概念算子理论方法。Gill教授的研究成果适用于自反性Banach空间上的线性演化，他提出去除自反性限制，允许最小域考虑，并将理论扩展到非线性演化。他计划就这些科学问题咨询专家，从而加强他的研究计划，并提高其效率水平，以获得进一步的资金支持。

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.