Related papers: Twisted partially pure spinors
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address some of them using a twistorial…
We solve the twistor equation on all indecomposable Lorentzian symmetric spaces explicity.
We review the twistorial structures by providing a setting under which the corresponding (differential) geometry can be described, by involving the $\rho$-connections. This applies, for example, to give new proofs of the existence of the…
A "Figure 8" shaped synchrotron is suggested for use in accelerating polarized protons in the energy range below ~ 20 GeV. The spin tune in such an accelerator does not ramp with energy and is equal to zero . Then the intrinsic spin…
We show that the $G_2$-manifolds and certain ${\rm Spin}(7)$-manifolds are endowed with natural Riemannian twistorial structures. Along the way, the exceptional holonomy representations are reviewed and other related facts are considered.
Each isometric complex structure on a 2$\ell$-dimensional euclidean space $E$ corresponds to an identification of the Clifford algebra of $E$ with the canonical anticommutation relation algebra for $\ell$ ( fermionic) degrees of freedom.…
Surfaces with concentric $K$-contours and parallel $K$-contours in Euclidean $3$-space are defined. Crucial examples are presented and characterization of them are given.
We define spin structures on perfect complexes outside of characteristic two, generalizing the usual notion for vector bundles. We give an explicit local characterization of spin structures, and show that for an oriented quadratic complex…
The closed homogeneous and isotropic universe is considered. The bundles of Weyl and Dirac spinors for this universe are explicitly described. Some explicit formulas for the basic fields and for the connection components in stereographic…
Exterior differential forms with values in the (Kostant's) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative…
We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form…
We explicitly describe all SO(7)-invariant almost quaternion-Hermitian structures on the twistor space of the six sphere and determine the types of their intrinsic torsion.
The tidally tilted pulsators are a new type of oscillating star in close binary systems that have their pulsation axis in the orbital plane because of the tidal distortion caused by their companion. We describe this group of stars on the…
We discuss hypercomplex and hyperk\"ahler structures obtained from higher degree curves in complex spaces fibring over ${\mathbb{P}}^1$.
The $sp(2M)$ invariant unfolded system is considered in the periodic twistor-like spinor space. Complete set of non-trivial charges corresponding to the global symmetry compatible with the periodicity conditions is constructed. Residual…
The paper studies explicitly the Hitchin system restricted to the Higgs fields on a fixed very stable rank 2 bundle in genus 2 and 3. The associated families of quadrics relate to both the geometry of Penrose's twistor spaces and several…
We emphasise the relation between the spin structure of the proton and the axial U(1) problem. New experiments motivated by the proton spin problem which could shed light on the nature of U(1) symmetry breaking in QCD are discussed.
Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.
In this paper, we introduce the new class of twisted $B$-splines and study some properties of these B-splines. We also investigate the system of twisted translates and the wavelets corresponding to these twisted $B$-splines.