The Boundary-Integral Formulation and Multiple-Reflection Expansion for the Vacuum Energy of Quantum Graphs

Vacuum energy and other spectral functions of Laplace-type differential operators have been studied approximately by classical-path constructions and more fundamentally by boundary integral equations. As the first step in a program of elucidating the connections between these approaches and improving the resulting calculations, I show here how the known solutions for Kirchhoff quantum graphs emerge in a boundary-integral formulation.