Related papers: Spinor Fields Classification in Arbitrary Dimensio…
An extended local Lorentz symmetry in four-dimensional (4D) theory is considered. A source of this symmetry is a group of general linear transformations of four-component Majorana spinors GL(4,M) which is isomorphic to GL(4,R) and is the…
The Lounesto classification splits spinors in six classes: I, II, III are those for which at least one among scalar and pseudo-scalar bi-linear spinor quantities is non-zero, its spinors are called regular, and among them we find the usual…
We extend the notion of super-Minkowski space-time to include $\mathbb{Z}_2^n$-graded (Majorana) spinor coordinates. Our choice of the grading leads to spinor coordinates that are nilpotent but commute amongst themselves. The mathematical…
The exterior algebra of Minkowski space naturally has the structure of a sixteen-dimensional Clifford algebra representation, and so can be used as the space of spinors. We examine plane, circular, and spherical solutions to the free Dirac…
The seven and nine dimensional geometries associated with certain classes of supersymmetric $AdS_3$ and $AdS_2$ solutions of type IIB and D=11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further…
It is shown how the old Cartan's conjecture on the fundamental role of the geometry of simple (or pure) spinors, as bilinearly underlying euclidean geometry, may be extended also to quantum mechanics of fermions (in first quantization),…
This paper is intended to describe twistors via the paravector model of Clifford algebras and to relate such description to conformal maps in the Clifford algebra over R(4,1), besides pointing out some applications of the pure spinor…
I begin by explaining how Riemannian geometry can be understood in terms of principal fibre bundles and connections thereon. I then introduce and motivate the definition of a spinor structure in terms of familiar geometrical ideas. The…
This study investigates the localization of spinor fields in braneworld models in six or higher dimensions. We study the relationship between fermions in spacetimes of $2n+2$ and $2n$ dimensions. In conformally flat extra-dimensional…
Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence…
We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of eleven dimensional supergravity. The metric, four form and Killing spinors are determined explicitly, up to an…
We give a spinorial characterization of isometrically immersed hypersurfaces into 4-dimensional space forms and product spaces $\M^3(\kappa)\times\R$, in terms of the existence of particular spinor fields, called generalized Killing spinors…
We reduce the classification of all supersymmetric backgrounds in eleven dimensions to the evaluation of the supercovariant derivative and of an integrability condition, which contains the field equations, on six types of spinors. We…
A spinor fields classification with non-Abelian gauge symmetries is introduced, generalizing the the U(1) gauge symmetries-based Lounesto's classification. Here, a more general classification, contrary to the Lounesto's one, encompasses…
We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the…
We summarize a unified and computationally efficient treatment of Fierz identities for form-valued pinor bilinears in various dimensions and signatures, using concepts and techniques borrowed from a certain approach to spinors known as…
We propose and develop a new method to classify orbits of the spin group ${\rm Spin}(2d)$ in the space of its semi-spinors. The idea is to consider spinors as being built as a linear combination of their pure constituents, imposing the…
The geometric Fierz identities are here employed to generate new emergent fermionic fields on the parallelizable (curvatureless, torsionfull) 7-sphere ($S^7$). Employing recently found new classes of spinor fields on the $S^7$ spin bundle,…
This paper proves that from the algebraic point of view ELKO spinor fields belong together with Majorana spinor fields to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class 5, according to…
Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong, together with Majorana spinor fields, to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class (5),…