Supersymmetric analysis of the spectral theory on in graphs. preprint (http://lagendra.s.kanazawa-u.ac.jp/ogurisu

We present a new approach to the spectral theory on innite graphs. We rst show that Laplacians on innite graphs can be treated in a frame-work of operator theory with supersymmetry. Using this supersymmetric structure, we rederive in a simple way known results as in Ref. [T. Shirai, Trans. Amer. Math. Soc., 32 (1999), 115{132] and to obtain new results. Our approach can be applied to discrete magnetic Schrodinger operators on innite graphs.