相关论文: Asymptotic spectral flow for Dirac operators

Let $P$ be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral boundary conditions and study the asymptotics of the heat trace of the associated operator of Laplace type.

Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by K.~Habermann. Here we study the spectral geometry aspects of these operators. In particular, we define the associated…

We show that the (graded) spectral flow of a family of Toeplitz operators on a complete Riemannian manifold is equal to the index of a certain Callias-type operator. When the dimension of the manifold is even this leads to a cohomological…

We analyze the action of the spectral flows on N=2 twisted topological theories. We show that they provide a useful mapping between the two twisted topological theories associated to a given N=2 superconformal theory. This mapping can also…

We define and study the noncommutative spectral flow for paths of regular selfadjoint Fredholm operators on a countably generated Hilbert C*-module. We give an axiomatic description and discuss some applications. One of them is the…

Callias-type (or Dirac-Schr\"odinger) operators associated to abstract semifinite spectral triples are introduced and their indices are computed in terms of an associated index pairing derived from the spectral triple. The result is then…

We analyze the limit of the spectrum of a geometric Dirac-type operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by the…

We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…

Establishing an exact relation for the derivative we show that the eigenvalue flows of the hermitean Wilson-Dirac operator obey a differential equation. We obtain a complete overview of the characteristic features of its solutions. The…

The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like…

We look at smooth manifolds equipped with a possibly singular Riemannian metric. We give sufficient conditions for the existence of scalar curvature measures and Dirac operators.

The necessary and sufficient conditions are given for a sequence of complex numbers to be the periodic (or antiperiodic) spectrum of non-self-adjoint Dirac operator.

Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here how the Dirac operator should be modified,…

The spectral flow of the overlap operator is computed numerically along a particular path in gauge field space. The path connects two gauge equivalent configurations which differ by a gauge transformation in the non-trivial class of…

We give the description of self-adjoint regular Dirac operators, on $[0, \pi]$, with the same spectra.

Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting…

There is a certain family of conformally invariant first order elliptic operators on Riemannian spin manifold which include Dirac operator as its first and simplest member. Their general definition is given and their basic properties are…

Recently we showed that the spectral flow acting on the N=2 twisted topological theories gives rise to a topological algebra automorphism. Here we point out that the untwisting of that automorphism leads to a spectral flow on the untwisted…

We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's…

We give an expression, in terms of boundary spectral functions, for the spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its domain is determined by local boundary conditions, and the manifold is of product type.…