The Maslov index: A functional analytical definition and the spectral flow formula
The authors develop the real and complex functional analysis of infinite-dimensional Lagrangians and give a new definition of Maslov index. This definition is given for any continuous path and does not require any deformations of the path, or assumptions at endpoints and crossings. Moreover the authors present an application of the new definition of Maslov index by developing the symplectic geometry of self-adjoint extensions of unbounded symmetric operators. Furthermore they give for a certain class of continuous families of unbounded Fredholm operators a rigorous definition of the spectral flow which is homotopy invariant. As a consequence they prove that the spectral flow is equal to the Maslov index of the corresponding family of abstract Cauchy data spaces. Note that the authors give an elementary, purely functional analytical proof of the spectral flow formula.
scientific article; zbMATH DE number 1207080