Monthly Archives: April 2025

Problem: Given a linear operator \(H\) on some vector space, define the resolvent operator \(G_H(E)\) associated to \(H\). Solution: The resolvent \(G_H(E)\) of \(H\) is the operator-valued Mobius transformation of a complex variable \(E\in\textbf C\) defined by the inverse: \[G_H(E):=\frac{1}{E1-H}\] … Continue reading →

Although Feynman diagrams are often first encountered in statistical/quantum field theory contexts where they are employed in perturbative calculations of partition/correlation functions based on Wick’s theorem, there is a lot of “fluff” in these cases that obscures their underlying simplicity. … Continue reading →