Related papers: A Calder\'on Problem for the Dirac operator with c…

We consider the Klein-Gordon equation on asymptotically anti-de Sitter spacetimes, and show that the forward Dirichlet-to-Neumann map (or scattering matrix) is a fractional power of the boundary wave operator modulo lower order terms in the…

This paper studies Dirac operators on end-periodic spin manifolds of dimension at least 4. We provide a sufficient condition for such an operator to be Fredholm for a generic end-periodic metric; this condition is shown to be necessary in…

This paper is devoted to the analysis of the single layer boundary integral operator $\mathcal{C}_z$ for the Dirac equation in the two- and three-dimensional situation. The map $\mathcal{C}_z$ is the strongly singular integral operator…

Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a…

In this paper, we obtain two Lichnerowicz type formulas for the Dirac-Witten operators. And we give the proof of Kastler-Kalau-Walze type theorems for the Dirac-Witten operators on 4-dimensional and 6- dimensional compact manifolds with…

We show the existence of a natural Dirichlet-to-Neumann map on Riemannian manifolds with boundary and bounded geometry, such that the bottom of the Dirichlet spectrum is positive. This map regarded as a densely defined operator in the…

In a previous paper we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kaehler manifolds. In the present article we show that the only manifolds in the limit case, i.e. the only manifolds where the lower bound is…

We clarify the structure obtained in H\'elein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle starting from a structure-less differentiable 10-manifold (arXiv:1508.07765v2…

On a compact spin manifold we study the space of Riemannian metrics for which the Dirac operator is invertible. The first main result is a surgery theorem stating that such a metric can be extended over the trace of a surgery of codimension…

I study the consequences of chiral symmetry restoration for the Dirac spectrum in finite-temperature gauge theories in the two-flavor chiral limit, using Ginsparg--Wilson fermions on the lattice. I prove that chiral symmetry is restored at…

We construct an explicit example of dimensional reduction of the free massless Dirac operator with an internal SU(3) symmetry, defined on a twelve-dimensional manifold that is the total space of a principal SU(3)-bundle over a…

We define two types of pseudo-differential perturbations of the Dirac operator within the framework of the noncommutative geometry. And we obtain the noncommutative residue of the inverse square of these perturbations on 4-dimensional…

We use Dirac operator techniques to establish a sharp lower bound for the first eigenvalue of the twisted Dolbeault Laplacian on holomorphic line bundles over compact K\"ahler manifolds.

The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare;…

Similarly as in AdS/CFT, the requirement that the action for spinors be stationary for solutions to the Dirac equation with fixed boundary conditions determines the form of the boundary term that needs to be added to the standard Dirac…

The purpose of this paper is to study harmonic spinors defined on a 1-parameter family of Einstein manifolds which includes Taub-NUT, Eguchi-Hanson and $P^2(C)$ with the Fubini-Study metric as particular cases. We discuss the existence of…

By analysing the work of Campolattaro we argue that the second Seiberg-Witten equation over the Spin^c_4 manifold, i.e., F^+_{ij}=< M,S_ij M >, is the generalization of the Campolattaro's description of the electromagnetic field tensor…

For $0<r<1$, let us consider the following annulus: \[ \mathbb A_r= \{ z\in \mathbb C\, : \, r<|z|<1 \}. \] A Hilbert space operator $T$ for which $\overline{\mathbb A}_r$ is a spectral set is called an $\mathbb A_r$-\textit{contraction}.…

We study functional determinants for Dirac operators on manifolds with boundary and discuss the ellipticity of boundary problems by using the Calder\'on projector. We give, for local boundary conditions, an explicit formula relating these…

A building block of noncommutative geometry is the observation that most of the geometric information of a compact riemannian spin manifold M is encoded within its Dirac operator D. Especially via Connes' distance formula one is able to…