Related papers: Dependence on the spin structure of the Dirac spec…
We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the sphere invariant. We study the notion of invariance of a spin structure and prove this…
In this paper we study the modular classes of Dirac manifolds and of Dirac maps, and we discuss their basic properties. We apply these results to explain the relationship between the modular classes of the various structures involved in the…
Let $M$ be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of $M$, and we derive a formula for the…
We describe Dirac structures on surfaces and 3-manifolds. Every Dirac structure on a surface $M$ is described either by a regular 1-foliation or by a section of a circle bundle obtained as a fiberwise compactification of the line bundle…
Classically, a spin structure on the loop space of a manifold is a lift of the structure group of the looped frame bundle from the loop group to its universal central extension. Heuristically, the loop space of a manifold is spin if and…
In this work the dynamics of a 2D Dirac oscillator in the spacetime of a magnetic cosmic string is considered. It is shown that earlier approaches to this problem have neglected a $\delta$ function contribution to the full Hamiltonian,…
We study the behavior of the spectrum of the Dirac operator on collapsing S^1-bundles. Convergent eigenvalues will exist if and only if the spin structure is projectable.
I begin with a general discussion about importance of constructing a picture of the nucleon in terms of QCD degrees of freedom, emphasizing the role of spin structure functions. I then give a short overview on the theoretical and…
We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension at least 5 the dimension of the space of harmonic spinors is no larger than it must be by the index theorem. The same result holds for…
In this article, we study the spectrum of the magnetic Dirac operator, and the magnetic Dirac operator with potential over complete Riemannian manifolds. We find sufficient conditions on the potentials as well as the manifold so that the…
We review recent progress in the understanding of the spin structure of the nucleon. For the free nucleon the issues addressed include the status of the Bjorken and Ellis-Jaffe sum-rules and the role of the axial anomaly. We outline recent…
We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.
Spinors are mathematical objects susceptible to the spacetime characteristics upon which they are defined. Not all spacetimes admit spinor structure; when it does, it may have more than one spinor structure, depending on topological…
Employing the $\mathbf{k}\cdot\mathbf{p}$ expansion for a family of tight-binding models for SmB$_6$, we analytically compute topological surface states on a generic $(lmn)$ surface. We show how the Dirac-cone spin structure depends on…
We review how RHIC is expected to deepen our understanding of the spin structure of longitudinally and transversely polarized nucleons. After briefly outlining the current status of spin-dependent parton densities and pointing out open…
This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in…
We investigate the effects of the chiral MIT boundary conditions for a Dirac particle in a 1D box. We show how the boundary condition affects the discrete momentum, energy level, transition frequency, and spin state in a box. The effects of…
In this paper we obtain exact solutions of a 2D relativistic Dirac oscillator in the presence of a constant magnetic field. We compute the energy spectrum and discuss its dependence on the spin and magnetic field strength.
I review the spin dependent structure functions which control dominant (twist-2) and sub-dominant (twist-3) phenomena in hard processes. Novel effects associated with chirally odd parton distributions and with transverse polarization are…
We shall give a twisted Dirac structure on the space of irreducible connections on a SU(n)-bundle over a three-manifold, and give a family of twisted Dirac structures on the space of irreducible connections on the trivial SU(n)-bundle over…