A Finite Element Approach to Feynman DiagramsPublic
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Feynman diagrams are essential tools used in the quantum field theory approach to condensed matter problems. It is typical to represent diagrammatic techniques in momentum space assuming implicitly that we have an infinite domain at hand. However, in finite nanoscale systems the momentum is not well-defined, so that the theory has to be reformulated. We espouse the coordinate space description, with the formalism having to satisfy geometric constraints of the physical domain. We show that the finite element method (FEM) is well suited for the quantum field theoretic modeling of nanoscale systems. The FEM uses a discretized physical domain that is faithful to the geometry at hand, and the wavefunctions are solved using a discretized form of the action and its variation.
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