The Boundary-Integral Formulation and Multiple-Reflection Expansion for the Vacuum Energy of Quantum Graphs
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2009
- DOI:
- 10.48550/arXiv.0907.3439
- arXiv:
- arXiv:0907.3439
- Bibcode:
- 2009arXiv0907.3439F
- Keywords:
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- Mathematical Physics;
- 34B45
- E-Print:
- 18 pages