Related papers: Dirac operator on spinors and diffeomorphisms

We give a formula for the first eigenvalue of the Dirac operator acting on spinor fields of a spin compact irreducible symmetric space $G/K$.

In this note, we consider the Dirac operator $D$ on a Riemannian symmetric space $M$ of noncompact type. Using representation theory we show that $D$ has point spectrum iff the $\hat A$-genus of its compact dual does not vanish. In this…

We show that for a suitable class of ``Dirac-like'' operators there holds a Gluing Theorem for connected sums. More precisely, if $M_1$ and $M_2$ are closed Riemannian manifolds of dimension $n\ge 3$ together with such operators, then the…

We numerically find out the spectrum of the $3$ spin $1$ Dirac operators found in~\cite{ApbPP}. We give an analytic and numerical proof that they are unitarily inequivalent. Since these operators come paired with an anticommuting chirality…

We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group.…

It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac…

We describe both the Hodge - de Rham and the spin manifold Dirac operator on the spheres ${\rm S}^3$ and ${\rm S}^2$, following the formalism introduced by K\"ahler, and exhibit a complete spectral resolution for them in terms of suitably…

The q-deformed fuzzy sphere $S_{qF}^2(N)$ is the algebra of $(N+1)\times(N+1)$ dim. matrices, covariant with respect to the adjoint action of $\uq$ and in the limit $q\to 1$, it reduces to the fuzzy sphere $S_{F}^2(N)$. We construct the…

We study two special cases of the equivariant index defined in part I of this series. We apply this index to deformations of Spin$^c$-Dirac operators, invariant under actions by possibly noncompact groups, with possibly noncompact orbit…

We show that, in round spheres of dimension $n\geq3$, for any given collection of codimension 2 smooth submanifolds $\mathfrak{S}:=\{\Sigma_1,...,\Sigma_N\}$ of arbitrarily complicated topology ($N$ being the complex dimension of the spinor…

Let $(M^{n}, g)$ denote a Riemannian spin manifold of dimension $n$ with Dirac operator $D$ induced from the Levi-Cevita connection acing on the spinor bundle, $S$ ($D$ is also called the Atiyah-Singer Operator). Let $c: Cl(TM^{n})…

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,…

In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…

For a Dirac operator $D_{\bar{g}}$ over a spin compact Riemannian manifold with boundary $(\bar{X},\bar{g})$, we give a natural construction of the Calder\'on projector and of the associated Bergman projector on the space of harmonic…

This work takes place over a conformally flat spin manifold (M,g). We prove existence and uniqueness of the conformally equivariant quantization valued in spinor differential operators, and provide an explicit formula for it when restricted…

Derivation of $\kappa$-Poincare bicovariant commutation relations between coordinates and 1-forms on $\kappa$-Minkowski space is given using Dirac operator and Allain Connes formula. The deformed U(1) gauge theory and appearance of an…

We define an equivariant index of Spin$^c$-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the index decomposes into irreducible representations according to…

We present a new description of the spectrum of the (spin-) Dirac operator $D$ on lens spaces. Viewing a spin lens space $L$ as a locally symmetric space $\Gamma\backslash \operatorname{Spin}(2m)/\operatorname{Spin}(2m-1)$ and exploiting…

This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…

We determine the structure of conformal powers of the Dirac operator on Einstein {\it Spin}-manifolds in terms of the product formula for shifted Dirac operators. The result is based on the techniques of higher variations for the Dirac…