The BoundaryIntegral Formulation and MultipleReflection Expansion for the Vacuum Energy of Quantum Graphs
Abstract
Vacuum energy and other spectral functions of Laplacetype differential operators have been studied approximately by classicalpath 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 boundaryintegral formulation.
 Publication:

arXiv eprints
 Pub Date:
 July 2009
 DOI:
 10.48550/arXiv.0907.3439
 arXiv:
 arXiv:0907.3439
 Bibcode:
 2009arXiv0907.3439F
 Keywords:

 Mathematical Physics;
 34B45
 EPrint:
 18 pages