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

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

2009-07-20

arxiv.org/abs/0907.3439v1

Physics

Mathematical Physics

18 pages

Scientific paper

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.

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