Related papers: Dirac generating operators of split Courant algebr…
We show that knowledge of the source-to-solution map for the fractional Dirac operator acting over sections of a Hermitian vector bundle over a smooth closed connencted Riemannian manifold of dimension $m\geq 2$ determines uniquely the…
In this paper we start from a basic notion of process, which we structure into two groupoids, one orthogonal and one symplectic. By introducing additional structure, we convert these groupoids into orthogonal and symplectic Clifford…
We introduce the Courant algebroid lift, a new construction that takes a Courant algebroid together with a vector bundle connection and produces, when the connection is flat in the image of the anchor, a Courant algebroid. In general, this…
In 1980 Michelsohn defined a differential operator on sections of the complex Clifford bundle over a compact K\"ahler manifold M . This operator is a differential and its Laplacian agrees with the Laplacian of the Dolbeault operator on…
The search for a geometric interpretation of the constrained brackets of Dirac led to the definition of the Courant bracket. The search for the right notion of a "double" for Lie bialgebroids led to the definition of Courant algebroids. We…
We consider on a spin manifold with boundary a Dirac operator $D_A$ with chiral boundary conditions, twisted by a unitary connection $A$. When $m$ is not in the chiral spectrum of $D_A$, we define an analogue of the Dirichlet-to-Neumann map…
Pre-Courant algebroids are `Courant algebroids' without the Jacobi identity for the Courant-Dorfman bracket. In this paper we examine the corresponding supermanifold description of pre-Courant algebroids and some direct consequences thereof…
The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…
In this thesis we develop the notion of LA-Courant algebroids, the infinitesimal analogue of multiplicative Courant algebroids. Specific applications include the integration of q- Poisson (d, g)-structures, and the reduction of Courant…
We introduce conformal Courant algebroids, a mild generalization of Courant algebroids in which only a conformal structure rather than a bilinear form is assumed. We introduce exact conformal Courant algebroids and show they are classified…
In this article we study the existence of solutions for the Dirac systems \begin{equation}\label{e:0.1} \left\{ \begin{array}{c} Pu=\frac{\partial H}{\partial v}(x,u,v) \quad\hbox{on} \ M, Pv=\frac{\partial H}{\partial u}(x,u,v)…
Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted…
We investigate with the help of Clifford algebraic methods the Mandelbrot set over arbitrary two-component number systems. The complex numbers are regarded as operator spinors in D\times spin(2) resp. spin(2). The thereby induced (pseudo)…
We introduce a $\mathbb{C}/\mathbb{Z}$-valued invariant of a foliated manifold with a stable framing and with a partially flat vector bundle. This invariant can be expressed in terms of integration in differential $K$-theory, or…
Motivated by Wigner's theorem, a canonical construction is described that produces an Atiyah-Singer Dirac operator with both unitary and anti-unitary symmetries. This Dirac operator includes the Dirac operator for KR-theory as a special…
Z2-gradings of Clifford algebras are reviewed and we shall be concerned with an alpha-grading based on the structure of inner automorphisms, which is closely related to the spacetime splitting, if we consider the standard conjugation map…
We construct bundles of modules of vertex operator algebras, and prove the rigidity and vanishing theorem for the Dirac operator on loop space twisted by such bundles. This result generalizes many previous results.
It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with…
Starting from an even definite lattice, we construct a principal circle bundle covered by a certain three-step nilpotent Lie group G. On the base space, which is again a nilmanifold, we then study the Dirac operator twisted by the…
The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4+4)-space. Split octonionic representation of SO(4,4) and Spin(4,4) groups and the trilinear invariant form are explicitly…