Viola Zhao L&S Math & Physical Sciences
Index Densities from Tropical Worldline Path Integrals
In general, quantum field theory describes the universe via nonlinear systems of partial differential equations. One current intriguing topic in theoretical physics is the asymptotic behavior of a quantum field theory. However, extracting information about this asymptotic behavior has posed a substantial challenge. Recently, tropical geometry has flourished as a new mathematical tool, which allows one to study the asymptotic behavior of a mathematical object, by translating nonlinear problems into vastly simpler piecewise linear problems at their asymptopia. For this project, the main objective is to construct a tropical notion of index density through the worldline path integral formalism and the tropicalization of path integrals using tropical geometry. Extracting a nontrivial index density would be a novel and enlightening contribution, essentially laying the mathematical foundations for differential methods in tropical geometry — an approach that has not yet been fully developed.
Message To Sponsor
I’m extremely grateful for your support of my SURF project this summer. The opportunity to participate gives me the chance to dive into a subfield I’ve not yet had the opportunity to explore. I deeply appreciate the resources and encouragement this program provides, and I’m excited to broaden my understanding of theoretical physics and mathematics.